On maximal repetitions in words
Identifieur interne :
000D81 ( PascalFrancis/Curation );
précédent :
000D80;
suivant :
000D82
On maximal repetitions in words
Auteurs : R. Kolpakov [
Russie] ;
G. Kucherov [
France]
Source :
-
Lecture notes in computer science [ 0302-9743 ] ; 1999.
RBID : Pascal:99-0526090
Descripteurs français
English descriptors
Abstract
A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first study maximal repetitions in Fibonacci words - we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and we mention some applications and consequences of this result.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
|---|
| A05 | | | | @2 1684 |
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| A08 | 01 | 1 | ENG | @1 On maximal repetitions in words |
|---|
| A09 | 01 | 1 | ENG | @1 FCT '99 : fundamentals of computation theory : Iasi, 30 August - 3 september 1999 |
|---|
| A11 | 01 | 1 | | @1 KOLPAKOV (R.) |
|---|
| A11 | 02 | 1 | | @1 KUCHEROV (G.) |
|---|
| A12 | 01 | 1 | | @1 CIOBANU (Gabriel) @9 ed. |
|---|
| A12 | 02 | 1 | | @1 PAUN (Gheorghe) @9 ed. |
|---|
| A14 | 01 | | | @1 French-Russian Institute for Informatics and Applied Mathematics, Moscow University @2 119899 Moscow @3 RUS @Z 1 aut. |
|---|
| A14 | 02 | | | @1 LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101 @2 54602 Villers-lès-Nancy @3 FRA @Z 2 aut. |
|---|
| A20 | | | | @1 374-385 |
|---|
| A21 | | | | @1 1999 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A26 | 01 | | | @0 3-540-66412-2 |
|---|
| A43 | 01 | | | @1 INIST @2 16343 @5 354000084584580310 |
|---|
| A44 | | | | @0 0000 @1 © 1999 INIST-CNRS. All rights reserved. |
|---|
| A45 | | | | @0 1 p.1/4 |
|---|
| A47 | 01 | 1 | | @0 99-0526090 |
|---|
| A60 | | | | @1 P @2 C |
|---|
| A61 | | | | @0 A |
|---|
| A64 | 01 | 1 | | @0 Lecture notes in computer science |
|---|
| A66 | 01 | | | @0 DEU |
|---|
| C01 | 01 | | ENG | @0 A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first study maximal repetitions in Fibonacci words - we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and we mention some applications and consequences of this result. |
|---|
| C02 | 01 | X | | @0 001D02A05 |
|---|
| C02 | 02 | X | | @0 001D02A01 |
|---|
| C03 | 01 | X | FRE | @0 Répétition @5 01 |
|---|
| C03 | 01 | X | ENG | @0 Repetition @5 01 |
|---|
| C03 | 01 | X | SPA | @0 Repetición @5 01 |
|---|
| C03 | 02 | X | FRE | @0 Longueur mot @5 02 |
|---|
| C03 | 02 | X | ENG | @0 Word length @5 02 |
|---|
| C03 | 02 | X | SPA | @0 Longitud palabra @5 02 |
|---|
| C03 | 03 | X | FRE | @0 Temps linéaire @5 03 |
|---|
| C03 | 03 | X | ENG | @0 Linear time @5 03 |
|---|
| C03 | 03 | X | SPA | @0 Tiempo lineal @5 03 |
|---|
| C03 | 04 | X | FRE | @0 Algorithmique @5 04 |
|---|
| C03 | 04 | X | ENG | @0 Algorithmics @5 04 |
|---|
| C03 | 04 | X | SPA | @0 Algorítmica @5 04 |
|---|
| C03 | 05 | X | FRE | @0 Maximal repetition in word @4 INC @5 72 |
|---|
| C03 | 06 | X | FRE | @0 Mot Fibonacci @4 INC @5 73 |
|---|
| C03 | 07 | X | FRE | @0 Mot binaire @4 INC @5 74 |
|---|
| N21 | | | | @1 340 |
|---|
|
|---|
| pR |
| A30 | 01 | 1 | ENG | @1 Fundamentals of computation theory. International symposium @2 12 @3 Iasi ROM @4 1999-08-30 |
|---|
|
|---|
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Le document en format XML
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<term>Maximal repetition in word</term>
<term>Mot Fibonacci</term>
<term>Mot binaire</term>
</keywords><front><div type="abstract" xml:lang="en">A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first study maximal repetitions in Fibonacci words - we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and we mention some applications and consequences of this result.</div>
</front><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0302-9743</s0>
</fA01><fA05><s2>1684</s2>
</fA05><fA08 i1="01" i2="1" l="ENG"><s1>On maximal repetitions in words </s1>
</fA08><fA09 i1="01" i2="1" l="ENG"><s1>FCT '99 : fundamentals of computation theory : Iasi, 30 August - 3 september 1999</s1>
</fA09><fA11 i1="01" i2="1"><s1>KOLPAKOV (R.)</s1>
</fA11><fA11 i1="02" i2="1"><s1>KUCHEROV (G.)</s1>
</fA11><fA12 i1="01" i2="1"><s1>CIOBANU (Gabriel)</s1>
<s9>ed.</s9>
</fA12><fA12 i1="02" i2="1"><s1>PAUN (Gheorghe)</s1>
<s9>ed.</s9>
</fA12><fA14 i1="01"><s1>French-Russian Institute for Informatics and Applied Mathematics, Moscow University</s1>
<s2>119899 Moscow</s2>
<s3>RUS</s3>
<sZ>1 aut.</sZ>
</fA14><fA14 i1="02"><s1>LORIA/INRIA-Lorraine, 615, rue du Jardin Botanique, B.P. 101</s1>
<s2>54602 Villers-lès-Nancy</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</fA14><fA20><s1>374-385</s1>
</fA20><fA21><s1>1999</s1>
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</fA45><fA47 i1="01" i2="1"><s0>99-0526090</s0>
</fA47><fA60><s1>P</s1>
<s2>C</s2>
</fA60><fA64 i1="01" i2="1"><s0>Lecture notes in computer science</s0>
</fA64><fA66 i1="01"><s0>DEU</s0>
</fA66><fC01 i1="01" l="ENG"><s0>A (fractional) repetition in a word w is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in w, that is those for which any extended subword of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w. We first study maximal repetitions in Fibonacci words - we count their exact number, and estimate the sum of their exponents. These quantities turn out to be linearly-bounded in the length of the word. We then prove that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and we mention some applications and consequences of this result.</s0>
</fC01><fC02 i1="01" i2="X"><s0>001D02A05</s0>
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</fC03><fC03 i1="01" i2="X" l="ENG"><s0>Repetition</s0>
<s5>01</s5>
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<s5>01</s5>
</fC03><fC03 i1="02" i2="X" l="FRE"><s0>Longueur mot</s0>
<s5>02</s5>
</fC03><fC03 i1="02" i2="X" l="ENG"><s0>Word length</s0>
<s5>02</s5>
</fC03><fC03 i1="02" i2="X" l="SPA"><s0>Longitud palabra</s0>
<s5>02</s5>
</fC03><fC03 i1="03" i2="X" l="FRE"><s0>Temps linéaire</s0>
<s5>03</s5>
</fC03><fC03 i1="03" i2="X" l="ENG"><s0>Linear time</s0>
<s5>03</s5>
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<s5>03</s5>
</fC03><fC03 i1="04" i2="X" l="FRE"><s0>Algorithmique</s0>
<s5>04</s5>
</fC03><fC03 i1="04" i2="X" l="ENG"><s0>Algorithmics</s0>
<s5>04</s5>
</fC03><fC03 i1="04" i2="X" l="SPA"><s0>Algorítmica</s0>
<s5>04</s5>
</fC03><fC03 i1="05" i2="X" l="FRE"><s0>Maximal repetition in word</s0>
<s4>INC</s4>
<s5>72</s5>
</fC03><fC03 i1="06" i2="X" l="FRE"><s0>Mot Fibonacci</s0>
<s4>INC</s4>
<s5>73</s5>
</fC03><fC03 i1="07" i2="X" l="FRE"><s0>Mot binaire</s0>
<s4>INC</s4>
<s5>74</s5>
</fC03><fN21><s1>340</s1>
</fN21><pR><fA30 i1="01" i2="1" l="ENG"><s1>Fundamentals of computation theory. International symposium</s1>
<s2>12</s2>
<s3>Iasi ROM</s3>
<s4>1999-08-30</s4>
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