[en] The binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. Based on this classical notion, we introduce the m-binomial equivalence of two words refining the abelian equivalence. The m-binomial complexity of an infinite word x maps an integer n to the number of m-binomial equivalence classes of factors of length n occurring in x. We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue-Morse word. We also mention the possible avoidance of 2-binomial squares.
Disciplines :
Mathematics
Author, co-author :
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Salimov, Pavel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words
Publication date :
2013
Event name :
WORDS 2013
Event place :
Turku, Finland
Event date :
from 16-09-2013 to 20-09-2013
Audience :
International
Journal title :
Lecture Notes in Computer Science
ISSN :
0302-9743
eISSN :
1611-3349
Publisher :
Springer, Berlin, Germany
Special issue title :
Combinatorics on Words
Volume :
8079
Pages :
217-228
Peer reviewed :
Peer reviewed
Commentary :
This is the long version corresponding to the submission (limited to 12 pages). It contains an appendix with the omitted proofs.
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