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I7K…B mk CB @ MB9gD3gDk CN0%$D †U

B ,-((.'R!#(!'%.6'&9( 1'Y. $%% G 2F$%&('#!('RGHI.k– 36#G|— &6#'!M1 .ML(%R('

& 6L(%.( "&($!'>.M(; 36#G ,-(L('#. /!'PN

h M9N CBXU MDqUg{7I % I7{ %

Lf h5h Pn3~8O:f.h5f*8n5f

t

1!$8 f e"! #.% f$<

P?IAT

τ

^{G' s€P} 8<(.(0.M(

t

^{= '"1(' 36G t}

t ∈ N

t KI D K

>A@

I 9"k CN0H

v

^LON

τ

^_

deg(v) ∈ {0, t}

f B @ @ W$ M% @ %

t

^{JR @ PSR7T W@ B B9gD3 @ r @ U.T M}

E ^(t)

^{U^V2EHG'T}

E m ^(t)

D]%gG …K

>A@

B.9 jB

@ @

WH

@

H

t

^{JR @ mP?RAT T}

m

^{P wR% @ Q}

Lf h5h Pn3, fm#&.4 4 l! 10fp<

=?>A@ ' mP?IAT

τ

^{B9 @ ƒW@ _}

.R K gD KI*BgDy_

DD k CN0%

w

I*EHG$KZNT @ gDdk CN0H $D

v

^{gT PSIKAT lD]}

w

^{k CN0H}

ƒBgT ' †U IATT SB @ a @ V

v

^{o t BpI D]B9.R K"BgD KIBgD LnN}

v

^JIEHG

w

B

@ I DcB.~r $VnI-G vB

@ k CN0% IAK…BgT…KIBXLnN

v

^JI*EHG

w

h "!OG'B'gDPSI7TxDy_

f

C;

h(τ)

^'gDPSIATdD

τ

^{D]SB.9 r $VnI-G B @ k CN0% IAK '^T wR DDH # KI*B}

LnNMB

@ a @

V2

r(τ)

^{U DV '^T P wI} BgDPSIATdDe_

h(τ ) := max

b

$&%('*)+$&,.-*/10''32(4,

τ

^{.R B^D KI*BgDjLON}

r(τ)

^JIEHG

b .

u0Q]{2D

KI*B

.R

4%>2.:,3' %('&.!

_ f

'8 0= + 243!K= 1'#&

LBL(τ )

^{D]SB59 @}

I D?B.9 ra]VnI7G /B

@ k CN.HmLONQB

@ a @

V VAT I7T WH^D]H ${*D…D]H^G'BQP wI

DD

τ

^{kBN0H PSIKAT t I sDFN}

deg(r(τ )) = 0

^{t DFN M}

LBL(τ) = 1

egf.hji`k]h4f.lB n+mo * %(( /36G

τ ₀

"3.$%<$%/'HC;

h(τ 0 ) = 0

^{3%36 ' '8 0=}

+ 243!K= 1'&

LBL(τ 0 ) = 0

^{#!$'K= B'$.M('J= 36#G}

τ 1 =

^{"3.7' C}

h(τ 1 ) = 1

^6'#!9('#

'8 = + 243!K= 1'&

LBL(τ 1 ) = 1

^N

egf.hji`k]h4f.l PnPo 7!' 8<(I.M(0.M'D,'"1' 36G

τ =

&%.

h(τ ) = 4

^6'!

LBL(τ ) = 3

^N

6 (%,"16G ('(:&($!'.('"/36G ;<(!#(' ' !*)*,?.+GHI.E'!L(:&(8''L(#'.(N

*BR6L((%'8<(.(0.M('R,'1' 36GH

τ

^{"3. ,-(8% / $' %'8} '"3R(Y.

3% B'#!(H!;,?!' 6 (%,"16G

τ 1

6'#!

τ 2

6'! ! B 6L(%*('(H( /.M.('

t

^='1'

36#GH

τ ⁰

,-(.ML>.('Y.M8('#! 3%$B'#!(7!6 %,"16G

τ ₁ ⁰ , τ ₂ ⁰ , . . . , τ _t ⁰

^N

1*2 . ! ( '$. <('!&B'P %L(I. L6 8('#'L(''P #>K(% B'!#( '7B'$.M(' 3. $J!(

36#2,<(%# 6#'! J%'6 (%,"16GH ('#(B'$.(' ('# ,?.MGHG.M )+63& ,?L((Y. b

,-($'!(( <(''R!6R!?+ 6'8Y.M7–

· · ·

—F!:3'&(!6#.M>. . O!"35 (' & 5( T;('& $'

h M9N CBXU MDqUg{7I % I7{ %

6 (%,"16G (' ,-.$ /?(' 0. N T I. ('#(' <$&(' !6 ! &(L(1%.(' 3'Y.M(' 6'! !9!3'>=

,-('&,?' )*'L(3% $%% !6#.M%Y./!'P <(%# 3' .(' $9&(L 1%.;/!'R6'#!

>J(%B('!PN

+G #38Y.AL(6 '$.M(('P <<(%# + $.$' ('@B'#! 'B'$.(' ' !( '8 0= -EY.M0=

1:!' 6'#&B('#'G G . ! &%&('Y.M%!<('Y.M8('!#: 3'Y.M/6'Y.M(,$J'H6'#! ! 4P3%

' !B$ ('Y.M0.3'#!('! 8&((,-('PN

egf.hji`k]h4f.l!PnPo '. 36#G GHI. ''6 (%,"16GH'PN +(,6 %,36G

τ 1

. &('"36( 36#2F&2)0. N

τ =

n

τ 1 τ 2

NN(N

τ n

=

2 n

j 1

τ 1,1 τ 1,2

N(NN

τ 1,j

τ 2

2

N(NN

τ n

B 80 ''' ,-($,"3 .('P !"35 2) ! (8<(I.M.M'

t

^{= '"1' /16G ;'#Y.3%% '"3. #%('}

4P3%(';3%7)*'L(3%'9$'/%1..M'9G. &%9'!PN &B('"36(

5 ]n) Pn+m

=?>A@

B9 T !T EHG'…r $VnI7G ;B

@ P wR%

@

'gD lEHG 9?

@ po @

W$ M%

@

%

t

^{JR @ dPSI7TxD}

τ

^M

D]%De_

kτ k ≡ 1 mod (t − 1).

egf:gf.h+io

:3L(&.('# '#243 '!68Y.M$',-(! C !: 36GH

τ

^N

CB A{ #NT$DeLT

@

I2${0

@

_

h(τ ) = 1

N9*3,?!(6#..(

τ =

^6'!

kτk = 1 + 0(t − 1)

^N

h(τ ) = 2

N';!(GGU3%%?G 65

τ =

t

. . .

'P "6#'!

kτ k = t = 1 + 1(t − 1)

^N

CB A{ #NT$D DFEHG @ _

/16G

τ ^(≤n)

^{G .O('( C $'GH3KGH3%}

n h τ ^(≤n)

≤ n

^&(%I.M

kτ ^(≤n) k = 1+i(t−1) i ∈ N

^N

K

τ

^{' 6'} (';8<(I.M(0.M

t

^{='"1($ 36G G .C}

n + 1

τ =

t

τ 1 τ 2

. . .

τ t .

h M9N CBXU MDqUg{7I % I7{ %

* 6 (%,"16GH

τ 1 , τ 2 , . . . , τ t

"3,-(' GH3KGH3%#'+C; #E$'

n

^N A*3!#('!68Y.$'0$36 =

>.ML6'& &%.<2)!6 (%,"16G

kτ j k = 1 + i j (t − 1),

^2)#

i j ∈ N

^6'!

j ∈ {1, . . . , t}.

7!#B)*'#L 3% ! /% 1..M/$'

τ

^&%I.

kτ k = X

1≤j≤t

kτ i j k

= X

1≤j≤t

1 + i _j (t − 1)

= t + (t − 1) X

1≤j≤t

i _j

= 1 + (t − 1) 1 + X

1≤j≤t

i _j

!

= 1 + i ⁰ (t − 1)

^{G .}

i ⁰ := 1 + X

1≤j≤t

i _j

^N

* )*'L(3% !C/% 1..M*$'

τ

^{%15.:R3%$9' !U$G}

kτk = 1 + i ⁰ (t − 1)

^GHI.

i ⁰ ∈ N

36!#8('O ?6'#! $GHI.7&%. 2)

τ

kτ k ≡ 1 mod (t − 1).

5 ]n) Pn

=?>A@ @ WH @ H

t

^{JR @ qP?RAT QlsT M}

t ≥ 2

^{o '} K^D]%"PgVDgG V7WsD|EHG B @ ra]VnI7G B

@

PS zRH

@

m

^{CBB @ r $VnI-G B @ ' @ k CN0H}

N

^_

m = 1 + (t − 1)N

^{UgV?9^G' DyWD*}

N = m − 1

t − 1 .

egf:gf.h+io

F(!#( B'$.M' '7( /.M.('

t

^{= '"1('3 36G} (;F$%<$% !*'''B'$.(';3%36;!

/%1..(!E,?.L. &'"36 ('(' K 3.( PL(6 !(G ('#7 3'Y.M K0.M(.%bO' 6 !'B 6L(% ,?I.ML.

8'' K 3.M(N +)+'L 3#% !( 3'Y.(' ' 'G 8<(I.M(0.M'

t

^{= '"1(' 36G 0. !GH'"3}

&%(

(N + m) − 1

^N

:3!( ''#(DB'$.(' ' 8<(.(0.M('

t

⁼ '"1(''/36G &'"36

t

'<"3. . ! )*'L(3%

!; 3'Y.(' 3'!(.ME&%(

tN

^N

tN = N + m − 1

⇐⇒ m = 1 + (t − 1)N.

h M9N CBXU MDqUg{7I % I7{ %

•7ŠX•9

Lf h5h Pn f Z h+i e #.% <

>2.M0.= 36G

sDD$ PSIKAT T MB

@

$D|EHGJI-KH

t

B2I7€"K

>A@C‚

yB '

@

Qk CN.H

v

^_

f @ { >A@ VgDDHa XLnN

v

^{V 'gTP wIYB^D ' †U IATdD T B @ a @ V2}

v

^{K > G @ > U @ BpI-D}

I7T WH^D]H ${*DSDDHgG CBk CBQB.gD*^DkBN0H $D

v

= N @

TI Z_…[

τ

^{KyN @ B.'% @ t eW @ V M% @ PSIKAT [}

v

^{U -U @ @ k CN0H}

LONT

τ

^{CB GQ}

deg(v) > 0

^p[P

p v

B @ KI*BLnN

v

^{VdBgT I7T W$ MH^D]% ${*D DDH^G'CBP zIK}

sT ' UAIAT T McB

@ a @

V

v

^{B2I7D=D]B @ KI*B t B @ D]%gG t CB^T LON}

v

^{IADEgG' CB}

sTdT @ B @ I7T WH^D]H ${*D…D]H^G'Bc[JNOG I D

I*EHG$KZN @ eWR7G M W@ B 2[

p ⁰ _v

^KIB

LONT

v

^{V '^T U -U PS zIjBgD# †U} IATdD"T MjB @ a @ V2

v

^{i MK >A@ I ' @}

k CN0%

v

^{CBK >A@ I} 9SDFN EHG KI*B

p ⁰ _v

|p v | ≤ |p ⁰ _v |,

D|NG' s€P

τ

^{2..0= 36G}

egf2% f*8`#&10 o T I.:!((+"'I.M$'D&%(J,-(!#(6#.('! &%.2)+3%%C '#$.M'

v

^{('(: >2.M.=}

36#GH* 1'& ! 8 #L(.('B &(B$'

v

^{L(6 'G /%3..*!(6} (%,"36GH

τ v

O!('

BR6L(%

v

^{. #.&%(}

LBL(τ v )

^N

- N9B(G. ! "'(.' >2.M.= 16G ,-(7!(! &('"32.(N

egf2% f*8`#&10 o #E!# '8 = + 243!K= 1'&(' ';'G 2 .0.= /36G

τ =

deg(r(τ))

τ 1 τ 2

N(NN

τ _deg(r(τ))

G .

deg(r(τ )) ≥ 2

^&%.

∀i : 2 ≤ i ≤ deg(r(τ))

LBL(τ i ) ≥ LBL(τ 1 )

.

^{VKNIQ !}

' # –

i

^{= (6#.˜— ?Nng#Q *2 N/"3.- N B(G.} 2F$%&('!#2 &'32. 2)7 2.0.= /16G H,- (' 4#(78?L((%%?2)

i = 2

^!

; Pnjm Uh&4 f2#15h0f*8(5`+-,& hzed4&#18-+7, f Z h+i

e"! #.% f

i

^{, h4f*8 o}

2

^<e<

[

τ

^{(PSI7T T B @ 5^KH#D]} $D|EHGJI-KH. @ D*TV&TI (I2 9YP wR% @ LONT

τ

^{B @ EHG 5^KH#D]}

PSR7T T M!'

@

Q]{2D

KI*B

.R cLnN

2

^{t DFN D]vB @ BpI @ IAD 'D]%gG' CBcPSI7T W9 B @}

gKH9sD]

PSIKAT f I @y> U @ GJIADD]S'D|NT EHG'~k NT$D] @ A{ #N B9

h M9N CBXU MDqUg{7I % I7{ %

egf.hji`k]h4f.lPn o E$'0.M6#8 .$' ('#( >2.M0.= 36G !69''

2

^{(.) >*/} /3LB&(L(J=

'>.M' >2.M0.= 36G

τ

^{!D( /.(.( ?'!G} 3%%B(''<% 1..M(

` µ

92)

1 ≤ µ ≤ 6

^!#6

4&M36 &(L(#'.5! 2.0.= /16G

τ ^(µ)

^{G . '2 '8 = + 243!K= 1'& $'}

LBL(τ ^(µ) ) = 2

(>.ML. <(!#('PN K !( 2..0= 36G

τ

^$E!#( 8<(.(6'&

` <sub>1</sub> ` 2

` ₃

` 4

` 5

` ₆

* !#6 !*-( V = 6#.= /.(6#'&+'Y.M.('!= >2.M.= 36G 8 ''Y.M !"3'' ,-(8% /

$H36('

` 1

LBL

=2

` 2

LBL =2

` ₃

LBL=2 ` 4

LBL=2 ` ₅

LBL

=2

` ₆

LBL

=2

h M9N CBXU MDqUg{7I % I7{ %

Lf h5h Pn3 f Z h+i

e"! #.% f ' 5`%M9 l4f #.&4 egf*)af.h+7,./#..0f2 <

=?>A@

U^D]#TxT HPSIATdKI7T B

@ gKH#D]

PSR7T W$

@

B ƒB.gD*

@ r @

U M KZN CB [\]T

U]N 9U V _

L (t,2t−1,...,1+t(t−1))

^{NpB @}

L ^(t,...)

UgVEHG'&B. SB

@ gKH#D]

PSR7T t B

@ dkBN0H

LnNOT i @ I*B

0

^t

t

^t

2t − 1

^t

3t −2

^{t D? NpB @}

1 + t(t −1)

^{DB f I-D G s€ t K >7@$‚ yB k CN.H}

v

'^D ^KH#sDD

PSIATdD

τ ∈ L (t,2t−1,...,1+t(t−1))

^{M _}

deg(v ) ∈ {0, t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)}.

h

L (t,2t−1,...,1+t(t−1)) m

N2B @

L ^(t,...) m

U^V2 EHG'T1B. K I 9 @ ^KH#sDD

PSRAT .T @ zI$UH

k CN0%

@

I*B

0, t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

^CB

m

^{P wR% @ X}

5 ]n) Pn

=?>A@ B9T !T EHG'Sr $VnI-G vB @ P wR% @ '^D lEHG'

D @ po ^KH#sDD

PSIATdD

τ

^{IADB @ K}

L (t,2t−1,...,1+t(t−1))

M&D]HTDy_

kτ k ≡ 1 mod (t − 1).

egf:gf.h+io

)*6#D( 2)('7!'< <(E!6 '#!68Y.M$' '3 !#(EC; # !#(; 36G

τ

^N

CB A{ #NT$DeLT @ I2${0 @ _

h(τ ) = 1

^{N9 E0.}

τ =

^6'#!

kτ k = 1 + 0(t − 1)

^N

h(τ ) = 2

^{N .}

τ =

λ

N(NN 6'!

λ

^{.('( !( (%36#,#.M'} B'$.M'&3!H36 !#( T ('&

{0, t, 2t − 1, . . . , 1 + t(t − 1)}

^)<$,?O$ /?('#Y.%H'H!(G U3%%

λ = 0

^{'Y. G. &% 0.8! N}

)*%%:!#(C '#$.M'&M3! ,?.L(' !B&2F$!.MC"$G

λ = 1 + k(t − 1)

^GHI.

1 ≤ k ≤ t

^N

CB A{ #NT$D DFEHG @ _

K

h(τ) > 2

"6'#!D(E&%.M

kτ ⁰ k ≡ 1 mod (t − 1)

^{2)E3%% 16#GH}

τ ⁰

^{G .}

h(τ ⁰ ) < h(τ)

^U!

3%$ ('B8 %('( C; # 3,?'D3%

τ

^N

*;/36G

τ

"3.E!:2F$%&('!"$G

τ =

λ

τ 1 τ 2

N(N(N

τ λ ,

6'! ! B 6#L(%,?.L. '' B'$.M('#&M3!

λ ∈ {t, 2t − 1, . . . , 1 + t(t − 1)}

^{N?)*%$ 8 ''#('}

λ

!"30.M%%';3%

λ = 1 + µ(t − 1)

^{G .}

µ ∈ {1, . . . , t}

^{N9 #3%%}

i ∈ {1, . . . , λ}

^&%.

• τ i ∈ L (t,2t−1,...,1+t(t−1))

• h(τ _i ) < h(τ)

h M9N CBXU MDqUg{7I % I7{ %

6'! '"3 !9'!68Y.M$'0$36.L(6'& &%I. 2) 3%% !

i

kτ i k = 1 + k i (t − 1)

^{G .}

1 ≤ k i ≤ t

^N

7!#B)*'#L 3% ! /% 1..M/$'

τ

&%I.7!"3G .

kτ k = X

1≤i≤λ

(1 + k i (t − 1))

= λ + X

1≤i≤λ

k i (t − 1)

= λ + (t − 1) X

1≤i≤λ

k _i

= 1 + µ(t − 1) + (t − 1) X

1≤i≤λ

k _i

= 1 + µ + X

1≤i≤λ

k i

!

(t − 1)

= 1 + k ⁰ (t − 1)

^{G .}

k ⁰ := µ + X

1≤i≤λ

k _i .

2.0.= /16G :GHI.

n

^{/% 1..M'P !# L(6 !(';(} /.M.('D,#'"1('3 16G (';&> 'P U"3.

- N B(G. Qf :,- 'P !"35 )*'L(3%B3FJGK.M$. &(&,?' . !6

t(n) ∼ αc ⁿ n ^−3/2

^GHI.

α = 0,25 . . .

^6'!

c = 2,74 . . .

^{*'U3& '3 !(C4P3#% ! >2.M.= 16G}

G .

N

''#('B'$.M' 6'!9'"3 'G 3"JG#.$.M' )*6!68H2) !(C4P3% /3 $' B' 6#.M;' ,#6'&36#2F&Y3,-XKNVKN)g%EgS Q S 9?N Q X!/&.M%%I. /$!'PN

*( &(,'./VWW#Q7$' *G $.3 S-36#2 >2.M.= 16G 7( /.(.,<$!'P J!L(6H('(

,-(%(,&('U3G %E('#243 (L((6#&.M: 16GHB&(> ('PN

- N B(G.96'Y.M6Y.+' 1P6#'! &fO' T;('&+$' 3!#!.'(+ 3M3G .(' 36#2 !(' >2.M0.=

16#GH'96'Y.M(!' (8<(I.M.M' ,'"1('/16G ('PNK)7!!.+ 33GH>.M '! 36G."33G >=

.M( ! 3!!I.MD("3%I.M('O !3#(5.!# R8J6#I !6 )7!!I.M$' $' )+' .(%('

!?BR6L((%"6#'!H!#(?6 %,"16G (GHI..(%' %3('ON :3L(6 &> 'H6#' .(<3'!'8,)>(D8,=6'#!

1 )>(D8,=IH:[-$W,.-.>

#

,.E5@0.$6.(DpQ$W)+)A(D*6'! ! c '*,5/ 46'! 36#.)*/ ! \^`@a6 c ,.-./!

2..0= 36GHN

<6 /"3 . ' IQ+f P!(+'Y.M6 6'&H36#2 ! 2..0= 16GHE' !(<U3G %7!/8<(I=

.M.('

t

='"1('3 16G :M3%%&GH'.(N

3('#! 36#2 !#(' 3!#!.'"&B .('AL(&.AE$&6(3 ' Q ?!35 !!#6'I..M%

C; H$' 2..0= 16GH' 3"JG#.$.M

n ^1/2

,-.M1&.( 6'#! (83'' ! L6&( & E$'K=

.M3'Y.M G .7$(;&B('"36#&8(.E3'&(,-('ON

'!M1('Y.M(0.:- N9B(G. GHI..(%= L(6&'!('K2F6'8Y.M$'(' ('T3 &%8(.( #!B #38Y.M'

)*'#L 3%('!( 2.M.0= 16#GH G .

n

'#'((''B'$.M('6'!

m

^{/% 1 ..M'P !#L(6('#(} ,?%(,&(' ('#243L(6&.(' 36G 243GH% &( 'P KL6,-(''PN9 !'-3%% !"35 ' 6<!+)*'L(3%

!/%1..M6'Y.M6# . <(!#(' $%% <&,#.9 36 (' )*"JG#.$.M8 2) ! )+'L 3#%:!(

2..0= 16GH*' !E'#243;L(6&.(' 36G 243G %E3'PN

- N$ G ,-(#(,#. ' IQ W 36#2 8$'0.M6#8 . BR( ('# Q -Q= E$(8?$'#!('L L '

( /.(.(' ,'"1(' 16GH' 6'!3 >2.M.=

2, 3

^{= /16G ('PN}

*( Q UQ= E$(-$'!#('L! ' !9$%&('#!(' )*,?.9(M3%%&(G ('#(./!' 36K2

(';Q -Q= +$(8?$'!('#LHL #(' 8<(.(0.M('

t

^{='"1(' 16G (' 6'! >2.M0.= 16G (' G .}

!' %36,#.M'B'$.M('#&M3!#('

t, 2t − 1, 3t − 2, . . . , t(t − 1)

^N

/1)2+V+2)/18#/6>*)a^& "!$#&%(')*,+"-/./0123#4-657!$#45 89: /6798b/1);!+$2)2/d8/1>?)=< 1e(*CT^R]+/d8+ e [

(3)?>*+>?+EF+E).

u0 P ^{AI2 HgD U gKH9sD]

PSRKAT

G F3 VWWgD8$''Y.M- N B(G. ' IQQ/''#$K <(I.M(&(#('!LKM3%%&GH'6'&;L(I=

&'P "$'A!#(E(' -(L3%I243%%P' 3'#!(' 6#'& !*' !((;*%$GH3,-(I.<M1('Y.(0.M'

&,'+!30.M(%%.(N

4O(I.M%.!"37L('Y.M3%C &(,'7!(7$%(&('!' *%$GH3,-(I.<$!($BGK= )*,?.

('Y..3'!('ON= (!( "3,?' ,-(G )+6#2F(,?' 6'! )*602F$G 6%(' !( &,'

36$-( '%'"&B'#!(';('&ZKL &(6'&'D&,?'P U$ !"35 !C*#%$GH3,-(I. .

.L.$&%(&.</!'D8 3''PN

1:,#/$#%7!G (.(' ('#"32 .%(' K(8 /O'Y.M% 6'&' !#98$G ,'3.M$(' &('K=

32 .M'D$' 2.M.0= 16#GH' 6'Y.(6'P P&,#.(*36D,-((%"32 .MBG.%(G ('Y.M(6#'&('

6'!;(G.E' .(6 6'&('A!(( :3.('0.M6#8 .6%bU(#BL(6GG<(8%P!:)*,?.7$'

/$ 6'!#3' Q f V "!B((!'K 33'Y.('9$' 2.M.0= 16#GH';6#'!;$'"J8J5%=

.('H36#2-#< &'J6#'& 3% L6&6'!%&('#!$:3.('0.M6#8 .6'H2)?+ $.1 .M8/30.M(%3'&('

6'Y.M6Y. N

* )*'#L 3% !D( /.(.(' ,'"1(' 16GH G .

m

^{/% 1 ..M' 6'! !R! 2.0.=}

2, 3

⁼

16#GHHGHI.

m

^{/%1..(' '#! &%P - N G ' Q} W/'"3#<(0. N ' /L((&. G . C+%2F:' U6#'8Y.M$'"3%,-(LJ6#'& 2)! ' 6G (3.M$ = L(6&('!'#2F6'8Y.$'' $' >2.M0.=

16#GH'P !9L(6 ('(U3G % ('K243 (L(6&.M(. 16GH9&(> ('P ('#9&Y3'L3-($'

!' ..M1.M'Pb !"36#' .( 241%%I. 36!;& %(#(I.<!#( )*'L(3%' !/8<(.(0.M('

t

^{='"1(' 16K=}

G G .

m

/%1..('D('(.M*6'! !( >2.M.=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

^{= 16#GHGHI.}

m

^<% 1..M(';3'!(.MN

*7GHI..M% !<"6'8Y.M$'"3%&% 6'&L(62)('!#/ <(7!($&B%GH1Y.M&8.<!(70=

<(.(0.M('

t

^{= '"1' 16G :G .}

m

^{<%1..M('6'! !$ 2.M.0=}

^t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

⁼

16#GHBG .

m

^{/%1 ..M'(! G} 2F$%&'!(';36#2)% 3'&(&(,-('PN

*( L('Y.M3%C"6'8Y.M$'"3%&% 6'&# K!B2)7! >2.M0.= 16G :'#'("3%, '7('K243 0=

L(6&.('3 36G 243G %7&%I. J0.73% -38 . SNS7(!&&(,-('PN <$ (!$J G .<#3.LBSN)g

!/ <(B&2)#.<(!(' 8 3''P OG'(' L(6#'"10.'#$K '""33U38Y.M' 6'! 4 ('K=

(&(,#' L(63GHG ('#&.M3&'(/!'PN

Lf h5h n+m Zh +-, f*8O)af2#.0 5f7e #&% % h+ljh4f2. +-, n fp% k 4mK<

[

F

^{' !yN @ B.'TH @ PSR7T t}

n ∈ N

^CB

T (n)

^{B. KYB @ PSRKAT &T M}

n

^{k CN0%}

' @ GJI UxB.gD3 @ "LON PSRAT

T (n) := {T ∈ F | T = (V,E) ∧ |V | = n}.

P ^V2EHG'

t(n) := |T (n)|

B9ra]VnI7G vB9gD3

@

PSR7T T M

n

^{k CN.HX f I G'€P B. @ V2T}

CB]KH${ #N

E(z) := X

n≥1

t(n) z ⁿ

' 6GHM3.$0= L(6&'!('K2F6'8Y.M$' $'

F

f dPSIATdKI7T 9

F

^{G' s€P '#243 L(6&. t KI D ^D @ zR @ MlwI JI \Q9sDFEHG' o = ]{'9N}

Θ(y) = 1 + P

i≥1

c _i y ⁱ

^T

c _i ∈ {0,1}

^CB

c _i = 1

^{K >A@}

i ≥ 2

^{UT M}

E(z) = zΘ(E(z))

egf2% f*8`#&10 o*D' ! )*,?. ,?>.MM3 ..(' 2.M.0=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

=

16#GHB80 '''A3%I.M('"3.HL(63*"'#.M$' VKNS !B 3%$+'Y.(G ('#& !( 46#'('&(M1'8=

.M'!: 2.0.= /16G ,-(,#.( P'#!(G ! (%36#,#.M'"B'$.M'&3! '&(#M1'8Y.<(!('P

36H3% ('$+'Y.MG ('&7!(&$!'#.M' /16G GHI. %36,#.M'. '#$.M'&M3!('

0 t 2t − 1

R*EHG #{0 MH DCB EHG

N(NN(

1+ t(t− 1)

,-.M3Y.M>.*/!'P '!(G 36 !( T ('& ' 6 ! 16#GH G . !* 2..0=

&'32.E(36&(6# .;/!'PN

*(' %.L.M' )+'M3.LB(02F$%&.$- N BGP /''D! >2.M0.= 16G :6'Y.M6Y. -!BL6

('(7,-(0.MGHG .(' U3G %('K243 (L(6&.M(; 16#GHB&> ('PN *B('#243 (L((6#&.M! 36G =

243G %

F (Θ 1 )

^GHI.7!(! "'('!'"6'8Y.M$'

Θ 1 (y) = 1 + X

1≤i≤t

y ^1+i(t−1)

0. &(M3!H!#-3GH% !( &($!'>.M' 16G HG . %36,#.(' B'$.M('#&M3!#('

0 t 2t − 1

N(NN(

1 + t(t − 1)

^{N *:T} '&:!#( ' !#((=-3GH% $8$G G ('!'( 2..0= 16GH

FL(Θ 1 )

0.!B#(7,-.M3Y..M T '&

L (t,2t−1,...,1+t(t−1))

^N

Lf h5h n

f

M[JEHG

@

†U W$ sD*

[z ⁿ ]A(z)

^{T B k N0 VD H LON @}

z ⁿ

^{B @ KZN @ T(I2 9 N0H $V @}

G'

A(z)

^D]

A(z) = P

n≥0

a n z ⁿ

^{t D|NI}

[z ⁿ ]A(z) = a n

' X P"3,-(' !:)*6K.M$('3& 3"3G; B'J6K.M 6'! + 3 .3'8 J(%:GH3.MG 3 .MBT;.M#$K!'

6'! K$&(' /(' ,?(,-('O P!L(6*)*'"3%WJ $' )*%&$I.MG (';6'!*3.M'.68Y.M6J=

'9' #.ML% ('98 '#'('PN>+'Y.M73'!G "3,?'9*369'&+!#('Y.MI.1.('2)=L(6&('J=

!'#2F6'8Y.M$'' G . /'$G 3%8$J L(('Y.M' 6'! ' L(6&(> &' &(%$'(' "$G ('

L(6#M3G GH'&>.MM3&('PN>B ,-('> .&' ('# !3 $' FJ&% N XK 6 3,-(%%PgYVJQ *! N

; njm Uh f0f.ie+7, l_i%i%f2 f `J8-% +-, <

f

@

V2T B$KH ${ #NT

P

n≥0 c+n−1

n

z ⁿ

UgDMVYB.9^D|EHG NOD D3'

= N @ T

1 (1−z) ^c

:3 2F$%&('!H'Y($'.($(G $' 3&M3'#&.! 6'# 6'Y.M 3'!#(G G. &%'P

!B)*'L(3% !E8<(I.M(0.M'

t

^{='1' 16GHBG .}

m

^{/%1..(';L6 ,-(('#('PN}

; n $0J8 $.0f.ie+-, f f*8 i%h i †J8-% f.l & $+7, l yl+fd#.&465=f24.0f:Ih+ 4m <

@ K >

M ' @

V2T B$KH ${ #NT

A(z) = P

n≥0

a _n z ⁿ

^{B.9 = ${ #NJI 9 EHG}

z = f (A(z))

^t

W NpU `K >A@

f

^{t B2I7€}

f(0) = 0

^CB

f ⁰ (0) 6= 0

^{t BpI sDD}

a n = [z ⁿ ]A(z) = 1

n [u ⁿ⁻¹ ] u

f(u) n

.

egf2% f*8`#&10 o #E!# 'Y "6'8Y.$'

f ^h−1i

!(E(3'&(&,?'('U6#'8Y.M$'

f

^G 6#5H&%I=

.M'

f (f ^h−1i (z)) = f ^h−1i (f (z)) = z.

BR('!>.*GH3'

f ^h−1i

^36#2 ,-(!#CK(I.M(';!:&B% 6'&

z = f(A(z))

^{3'P $ 2F$%&.}

f ^h−1i (z) = f ^h−1i (f (A(z)))

= A(z).

R*EHG #{0 MH DCB EHG

*U6#'8Y.M$'

A(z)

^{.E3%$ !+G} 8(#2F6'8Y.$' $'

f

^N

' !" .(M3 .M6;0.A!"3 3&M3'&( 'Y$'0.M$G $2.D36 #%L. GHI.;!(

+G 82F6#'8Y.M$'0= A+$.M3.M$' 3'&&(,-('<$!'Pb (L(6#G/((% /$G .M>. &g# %K(I.MQ SRf / N N

5 ]n) n+m

f ra$VeI7G B @ @ WM% @ H

t

^{R @ mPSRKAT T M}

m

^{P wR% @ D]}

E _m ^(t) = 1 m

t ^m−1 _t−1

m−1 t−1

.

egf:gf.h+io

*B(8<(I.M.M'

t

⁼ '"1'/16G :2F$%&'9!("KG ,?$%('& %(J6#'&

T = +

t

T T

NN(N

T ,

6'! 2) ! L(6&('!'#2F6'8Y.$'

T (u) = P

m≥0

a _m u ^m

^{!H)+'L 3%}

a _m

^{!#((. 16#GH G .}

m

^{<% 1..M(' &%I.}

T (u) = u + T (u) ^t .

^{4SNIQ !}

:3G . &%. 36#

u = T (u)−T (u) ^t = f (T (u))

^{G .}

f(z) = z −z ^t

^{N 0.}

f ⁰ (z) = 1−tz ^t−1

^6'#!

f (0) = 0

^$

f ⁰ (0) = 1 6= 0

^{N *6#} )*'#<('!6#'&R!#(7 3&3'&' ' ($'2F$GH%

U38Y.HSNV ! "3%.M' 2) ! )+'L 3#%+! 8<(.(0.M('

t

='"1('/16G G .

N

^''#('

B'$.(';6'!

m = 1 + (t − 1)N

^{/% 1 ..M'}

E _m ^(t) = [u ^m ]T (u)

= 1

m [u ^m−1 ] u

u − u ^t m

<(&'U38Y.SNV

= 1

m [u ^m−1 ]

1 1 − u ^t−1

m

= 1

m [u ^m−1 ] 1 (1 − u ^t−1 ) ^m

= 1

m [u ^m−1 ] X

i≥0

m + i − 1 i

u ^(t−1)i

<(&'U38Y.SNIQ

= 1

m [u ^(t−1)N ] X

i≥0

m + i − 1 i

u ^(t−1)i

^!''

m = 1 + (t − 1)N

= 1 m

m + N − 1 N

E$KHL' .+3';! J.M%%

i = N

^N

R*EHG #{0 MH DCB EHG

*6D'B%.ML>.MC .ML6'&

N = ^m+1 _t+1

^(&,#.7

E _m ^(t) = [u ^m ]T (u) = 1

m

t ^m+1 _t−1

m+1 t−1

.

^{4SNV !}

5 ]n) n

[

T ^h−1i (u)

^{B9 @ vI sD}

T ^h−1i (u) := u − u ^t

T ^h−1i (u)

^{D] B.9 L @ D3 = ${ #NXLONT}

T (u)

egf:gf.h+io

B <(!#(' ! 3&3'& ' ($'2F$GH%/36#2!"6'8Y.M$'

T ^h−1i (u) = u − u ^t

^3'K=

<('!'P -6'! 3%7!'EGH8(02F6'8Y.M$'

T ^h−1ih−1i

^!;

T (u)

#(M360.M(%%'PN

T ^h−1i (u) = u − u ^t

= X

j≥0

a _j u ^j

^GHI.

a ₀ := 0 a ₁ := 1 6= 0 a _t := −1

^6'!

a _j := 0

^$'.(N

+G !E$KHL' .(';!( EGH8(02F6'8Y.M$'

T ^h−1ih−1i

^$'

T ^h−1i

^{L(6 ,-((''P /'!('}

' 6';!C 3&3'& 'Y$'02F$G (% 3'

[u ^m ]T ^h−1ih−1i (u) = 1

m [u ^m−1 ]

u T ^h−1i (u)

m

= 1

m [u ^m−1 ] u

u − u ^t m

= 1

m [u ^m−1 ]

1 1 − u ^t−1

m

= 1

m [u ^m−1 ] 1

(1 − u ^t−1 ) ^m .

A+6#' 6,..6

v := u ^t−1

^{N :3G .7&%.}

u = v ^{t−1 1}

^$

u ^m−1 = v ^{m−1 t−1}

^N K6#,..M6#(/.M0=

'

N := ^m−1 _t−1

^{N%:3G .O&%I. 36}

m = 1+(t−1)N

6#'!P80 ''' G .P!#(('C/L((' 6'&'

#(,?'

[u ^m ]T ^h−1ih−1i (u) = 1

m [v ^N ] 1 (1 − v) ^1+(t−1)N

= 1

m [v ^N ] X

j≥0

1 + (t − 1)N + j − 1 j

v ^j

/&('-38 .S#NQ

= 1 m

1 + (t − 1)N + N − 1 N

+$J / N",?

j = N

R*EHG #{0 MH DCB EHG

= 1 m

tN N

= 1 m

t ^m−1 _t−1

m−1 t−1

= [u ^m ]T (u)

/&('& % N FSNV!>N

*U6#'8Y.M$'('

T ^h−1ih−1i (u)

^6'!

T (u)

^{0.MG G (' ' 3%%'A#(' E$KHL' .(' ,-('P O}

'! 3%$ !' .PN

B <(!(' '"3'."$GH% 2) ! '!% &$GH>.M# J6GHG ,-('> .&'PN TD3'

8 3'' ' K(%(' &6'!#%(&('!' TD3.(GH3.8 %,>#(' $J!( A*3%3& <(8(' "'#!('P

$ L(6#G /((%'VKQU$J! ' VS N './ / 8 3'' !(8Y. T 6%I.M5%83 .M$' !=&B% 6'&

G .

(q−1)

^6'!)*6G 6%I.M#%L('!-$J!( 36!6$%%0.1'#!& '!68Y.M$' &2)#. /!'PN ; n Lf*% fn80h+ie+7, fX5`#.% % f & +-, <

=?>A@ I2 9

q ∈ R

t

q 6= 1

^{CB I 9}

n ∈ N ₀

^{M _}

X n

i=0

q ⁱ = q ⁿ⁺¹ − 1 q − 1 .

' # & %( 6'#&DQ+g %..;- N B(G.A(' 3%%&(G ('#U6#'8Y.M$'"3%&%( 6'& (+2): >2.M0.=

16#GH #!*L(69'<B%3:'#2439(L(6&.M($/16G *&> 'PN9*(/(LJ6#'& .M%%I. !'

L('Y.MM3%('.+ 6'8Y. !D< <((!"3 !"35B!#7,-(!#(' 36#GH8 %3'

E m ^(t)

6'!

L (t,2t−1,...,1+t(t−1)) m

&%(#G 1Y.& '!PN

; n 1#&; h Sl0l4fh+-,/#&10 18 f Z5hji

e"! #.% f +-, f2% k <

[

`(m)

B.9Yra]VnI7G /I @ gKH9sD]

PSRKAT

τ ∈ FL (Θ)

^{T M}

m

^{P zRKH @ t B.SV ' @Y= I-T 9}

$KI*EHG @ V2T %

@

PSRKAT

F (Θ)

^{^G ! @ SD3}

L(u) := P

m≥1 `(m) u ^m

^{B.mBpI-V ^G ! @}

@ V CB $KH${ #NQ

L(u)

^{@ K > M B. = ${ #NJI 9 EHG}

L(u) = u + L

u Θ (L(u)) − 1 L(u)

.

%

@

B

@

N @

I7D D*TV

c 1 := [y]Θ(y) = 0

^{UnWsDD =Ck gT t} BpI-€mB.9^D*

=

${ 9NJI2

EHG B9 .!ODD U^DV

t

B.9

L(0) = 0

^{@ K > M}

*3"$!(6'& !35R!#(+$J L(('Y. $

y

^'

Θ(y)

^{&%( W ' $%% 8&(%I.} !"3,-(!

6 3.M3:!( K!"35 !E)*'#L 3%?!(= 16G *G .

m

/%1..('&('36!"3'#'('!#% .( #/'' B'$.(' $G &BM3! Q '#Y. %36,#. '!ON *3D,?!H'R!()*,?.,?>.MM3 ..(' 36G =

8 %3' !(; 'M1'8 6'& 2)%%'P Y$%%G 2F$%&'!'H!(+)+''"3G &(%I.M'P 36./''

B'Y.E %L.78/1'Y.;!PN

R*EHG #{0 MH DCB EHG

T I. !#((' C+%I2FG ..M(%':8 ''('! .L. !(' / <( 2)#('O !35+!#<T ('#&<!#( (8<(I.M.M'

t

^{='1'/16G GHI.}

m

^{/%1..(' 6#'!} !T;('&!? 2.M.0=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

⁼

16#GHBG .

m

^{/%1 ..M' &%(#G 1Y.& '!PN}

5 ]n) n

f

ra]VnI7G ƒB

@ @

WM%

@

H

t

^{JR @ XPSRKAT T}

m

^{PS zRH @ ' @ D* MD CBXB @ ^KH#sDD}

PSR7T cT M B @ zI$UH k CN0% @ I*B

t, 2t − 1, . . . , 1 + t(t − 1)

^{T M}

m

^{P wR% @ mI2CB}

@ @ D3MD DB EHGQ

egf:gf.h+io

*7 2.M.0= 16#GH 36

L (t,2t−1,...,1+t(t−1)) m

'#! ('#'6 %GH'& !#(U3G % !(:'#243 0=

L(6&.('/16G

F (Θ)

^GHI.

Θ(y) = 1 + P

1≤i≤t

y ^1+i(t−1)

^N

! L(6&('#!('#2F6#'8Y.M$'

L(u) = P

m≥1

|L (t,2t−1,...,1+t(t−1))

m |u ^m

2)# !#)*'L(3%U!D >2.M0.=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

= 16#GH9G .

m

^{/%1 ..M' '}

L ^(t,...) m

&%. !"6'#8 .$'3%&%(=

6'& U38Y.SNS !

L(u) = u + L

u Θ(L(u)) − 1 L(u)

.

!B,?>.M3Y.M.('" >2.M0.=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

^{= 16G 0.! ,-(#(,?'!}

"6'8Y.M$'

Θ

&(&,?' !6#

Θ(y) = 1 + P

1≤i≤t

y ^1+i(t−1)

^N *3(.<<(.(

L(u) = u + L



  u P

1≤i≤t

L(u) ^1+i(t−1) L(u)



 

= u + L u X

1≤i≤t

L(u) ^i(t−1)

! ,

6'!;(&,#.&'"36;('# 6'&

L(u)

^{G .}

L(0) = 0

$36&(>.ML>. U!"35

c ₁ := [y]Θ(y) = 0

^N

A+6#' .

T (0) = 0

^6'!

u + T u X

1≤i≤t

T (u) ^i(t−1)

!

= u + T (T (u) − T (u) ^t ) X

1≤i≤t

T (u) ^(t−1) i

!

/&('& % N FSNQ5!

= u + T (T (u) − T (u) ^t ) X

0≤i≤t

T (u) ^(t−1) i

− 1

!!

R*EHG #{0 MH DCB EHG

= u + T (T (u) − T (u) ^t ) (T (u) ^t−1 ) ^t+1 − 1 T (u) ^t−1 − 1 − 1

!!

/&('U38Y.SN)g

= u + T (T (u) − T (u) ^t ) (T (u) ^t−1 ) ^t+1 − 1 − (T (u) ^t−1 − 1) T (u) ^t−1 − 1

!

= u + T T (u)(1 − T (u) ^t−1 ) T (u) ^t−1 − (T (u) ^t−1 ) ^t+1 1 − T (u) ^t−1

!

= u + T

T (u)

T (u) ^t−1 − T (u) ^{t 2 −1}

= u + T

T (u) ^t − T (u) ^{t 2}

= u + T T (u) ^t − (T (u) ^t ) ^t

= u + T T ^h−1i T (u) ^t

/&('#3.L S#NV

= u + T (u) ^t

= T (u)

<(&'"&B% N FSNIQ !>N

*$U6#'8Y.M$'

T (u)

^(02)%%I. 3%$B!$"6'8Y.M$'"3%&% 6'& ! 2) !< 'J6#GHM3.$0= L(6&('J=

!'#2F6'8Y.M$'9!< 2.M.0=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

⁼ 16#GH+&%I. bY!"3/,?!(6#..(

T ≡ L

^N

BR(%E3%$ !3 ' 6GHM3.$0= L(6&'!('K2F6'8Y.M$'

T

^{! ( /.(.('}

t

^{= '"1(' /16G 6'#!}

! ' 6G (M3 .M$ = L(6&'!'#2F6'8Y.M$'

L

^{!( 2.M.0=}

^t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

^{= 16K=}

G !#('Y.M '!P +'! 2F$%&% 36 !R)*'L(3%!(A8<(I.M(0.M'

t

='"1('/16G G .

m

^/%1..('6'! !# )*'L(3%#!#( >2.M0.=

t, 2t − 1, 3t − 2, . . . , 1 + t(t − 1)

^{= 16G GHI.}

m

^<%1.0=

.M';&%PN

';!(G )*,'..</!'D' 6';!B)+,,%!6'#&('

LE

^6'!

EL

!#"'(0. N9:3,? ,%!.

LE

('(' >2.M.= 36G

τ ∈ L (t,2t−1,...,1+t(t−1)) m

36#2 ('#(' ( /.(.('

t

^{= '"1(' 36#G}

LE(τ) ∈ E m ^(t)

3,P "6#'!

EL

^{! D3% !C+G} 8(#M3,,#%!#6'& $'

LE

#(M360.M(%%'

−−−→ LE

L (t,2t−1,...,1+t(t−1))

m ←−−− E m ^(t)

EL

:3,-( $%% 2)*,?! )+,,%!6'#&(' &%.(' ?. ('" 36#G

τ

^{$ <$% '}

L (t,2t−1,...,1+t(t−1)) m

3%

36;'

E m ^(t)

$ 0.

LE(τ) = τ

^6'#!

EL(τ ) = τ

^{N *3(5. 2F$!#('}

LE

L ^(t,...) m ∩E m ^(t)

= EL

L ^(t,...) m ∩E m ^(t)

= id .

)*6#&('!;$';!7)*,,%!6#'&$I2. !#- N>B(G. ' Q WP2)

t = 2

,-((,-(';"3.

!A!K(3%%&(G ('(6'& L(6'"1. ,-((%32.+2)#

t = 3

^6'!

t = 4

!6#&>2)0. 6'!

!"3'3;2)#+3%%&(G ('#(

t

^{2F$G 6%(.(N}

Š  MŽ  ,*p‰ < 77

t = 2

+G '!/8Y.M$' L #(' ( /.(.('A,#'"1(' 16G (' GHI.

m

^/%1..M'P

τ ∈ E m ⁽²⁾

U6'#!

2..0=

2, 3

^{= 16#GH' G .}

m

^/%1..('O

τ ⁰ ∈ L ^(2,3) m

L(6 (.(%%('P "3.- N G ' Q W !

2F$%&('!#(' )*,,#%!#6'&';!#"'(0. N

4)Z! *6 3'02F$GH3.M$'

: L ^(2,3) m → E m ⁽²⁾

0.8J6#I9! "'.

4)Q !

( ) :=

^b

4):V !

τ 1 τ 2

:=

_{(τ 1 )}

_{(τ 2 )}

^b

4) ga!

τ 1 τ 2 τ 3

:=

_{(τ 3 )}

_{(τ 2 )}

(τ 1 )

^N

. rbU$U B

! *6 3'02F$GH3.M$'

: E m ⁽²⁾ → L ^(2,3) m

#+!'* "'I.M$'D!-$8 Y.6'&9,-('> .&'3+''”– K#'.. —!6 ('('A0=

<(I.M(0.M' ,'"1'2 36G !E$&('"3'#' .

L

= *(8$G-$.M$'PN - N B(G.H! "'(.<!(

L

⁼ +(8$G-$I.M$'2B2F$%&.

Lf hz h Pn+mm

L

Lf % k i hz h 18 f*8n:gf.hz5f*8O fb9]h.!]80f:e"! #.% f $+7,4m <

BgT k CN0%

x

^{'^D @ WH @ H U2JR @ PSI7TxD}

τ ∈ E ⁽²⁾

^t

kτk > 1

^{t W@ B '}

I @ {.9 @

ξ(x)

^{V2yN @ B.'T P jB2I$U .I B @ a @ V}

r

^{B^DPSIATdD}

τ

= I sDUB~[ !OG'bLnN

r

^{@ ck CN.HDCB t D3V}

ξ(r) := 0

^JD|N]D]

ξ(r) := 1

h

= I sDYB

@

I%

@

gD?k CN.H]D

x 6= r

^{B.9 I @ {.9 @}

0

^{UgDV CBU BS[ !OG}

LnN

x

^{@ ck CN.HDCB t D3V}

ξ(x) := 0

^JD|N]D]

ξ(x) := 1

P ^V2 EHG' ' mB @ WH @ H U JR @ (PSIAT T MvB @ a @ V2

r

^{t B @ IKAD}

τ

^{DDH^G' t}

CBgT I 9kBN0H K

@ W$

@

B t B

@

I%

@ T M

1

^{TI @ {. @ :sDD t I sD}

τ ⁽⁰⁾

^{/[ 9}

` <sub>1</sub> , ` ₂ , . . . , ` _kτ (0) k

B. P wR% @ LON

τ ⁽⁰⁾

^{Q${*D yEHG D „ @ B. …W@ UgVEHG' B}

@ WM% @ H U R @ P?IAT T M B @ a @ V

` i

I sD

τ ⁽ⁱ⁾

^{t K >A@}

1 ≤ i ≤ kτ ⁽⁰⁾ k

f

L

= *(8$G.?$.$'

B^DPSIATdD

τ

^{U^D]H^G SBpI2 IADB @= N}

σ _τ := τ ⁽⁰⁾ , τ ⁽¹⁾ , τ ⁽²⁾ , . . . , τ ^{(kτ (0) k)} .

F>.ML.E8 3'';!B)*,,%!6#'& J(8 6I9!'.$/!'

+Q !

( ) := ;

V ! *( 36#G

τ ∈ E m ⁽²⁾

"3,-B!

L

⁼ +(8$G-$I.M$'

σ τ = τ ⁽⁰⁾ , τ ⁽¹⁾ , . . . , τ ^{(kτ (0) k)} ,

6'!

` <sub>1</sub> , ` ₂ , . . . , ` _kτ (0) k

(' !</%1..( $'

τ ⁽⁰⁾

^{'' '8 0= -E .0= 1B!' 6'&N}

:3'';0.

(τ) :=

(τ ⁽⁰⁾ )

τ _{i 1}

` _{i 1}

τ _{i 2} ` i 2

N(N(N

τ i _{kτ (0) k}

` _i

kτ (0) k

.

:3,-( 0.72)

1 ≤ p ≤ kτ ⁽⁰⁾ k

τ i p :=

 

 

 

 

 

 

 

 

 



` i p

(τ ⁰⁰ )

243%%

τ ^{(i p )} =

` i p

τ ⁰⁰

;

` i p

(τ ⁰⁰ )

(τ ⁰ )

243%%

τ ^{(i p )} =

` _{i p}

τ ⁰ τ ⁰⁰

.

XKNIQ !