scholarly journals k-Abelian Equivalence and Rationality

2017 ◽  
Vol 154 (1-4) ◽  
pp. 65-94 ◽  
Author(s):  
Julien Cassaigne ◽  
Juhani Karhumäki ◽  
Svetlana Puzynina ◽  
Markus A. Whiteland
Keyword(s):  
Abelian Equivalence

scholarly journals On a generalization of Abelian equivalence and complexity of infinite words

2013 ◽  
Vol 120 (8) ◽  
pp. 2189-2206 ◽  
Author(s):  
Juhani Karhumaki ◽  
Aleksi Saarela ◽  
Luca Q. Zamboni
Keyword(s):  
Infinite Words ◽  
Abelian Equivalence

scholarly journals The binomial equivalence classes of finite words

2020 ◽  
Vol 30 (07) ◽  
pp. 1375-1397
Author(s):  
Marie Lejeune ◽  
Michel Rigo ◽  
Matthieu Rosenfeld
Keyword(s):  
Nilpotent Group ◽  
Equivalence Class ◽  
Free Monoid ◽  
Equivalence Classes ◽  
Single Element ◽  
Free Nilpotent Group ◽  
Context Free ◽  
Abelian Equivalence

Two finite words [Formula: see text] and [Formula: see text] are [Formula: see text]-binomially equivalent if, for each word [Formula: see text] of length at most [Formula: see text], [Formula: see text] appears the same number of times as a subsequence (i.e., as a scattered subword) of both [Formula: see text] and [Formula: see text]. This notion generalizes abelian equivalence. In this paper, we study the equivalence classes induced by the [Formula: see text]-binomial equivalence. We provide an algorithm generating the [Formula: see text]-binomial equivalence class of a word. For [Formula: see text] and alphabet of [Formula: see text] or more symbols, the language made of lexicographically least elements of every [Formula: see text]-binomial equivalence class and the language of singletons, i.e., the words whose [Formula: see text]-binomial equivalence class is restricted to a single element, are shown to be non-context-free. As a consequence of our discussions, we also prove that the submonoid generated by the generators of the free nil-[Formula: see text] group (also called free nilpotent group of class [Formula: see text]) on [Formula: see text] generators is isomorphic to the quotient of the free monoid [Formula: see text] by the [Formula: see text]-binomial equivalence.

scholarly journals k-Abelian Equivalence and Rationality

2016 ◽  
pp. 77-88 ◽  
Author(s):  
Julien Cassaigne ◽  
Juhani Karhumäki ◽  
Svetlana Puzynina ◽  
Markus A. Whiteland
Keyword(s):  
Abelian Equivalence

scholarly journals On cardinalities of k-abelian equivalence classes

2017 ◽  
Vol 658 ◽  
pp. 190-204 ◽  
Author(s):  
Juhani Karhumäki ◽  
Svetlana Puzynina ◽  
Michaël Rao ◽  
Markus A. Whiteland
Keyword(s):  
Equivalence Classes ◽  
Abelian Equivalence

scholarly journals Abelian maximal pattern complexity of words

2013 ◽  
Vol 35 (1) ◽  
pp. 142-151 ◽  
Author(s):  
TETURO KAMAE ◽  
STEVEN WIDMER ◽  
LUCA Q. ZAMBONI
Keyword(s):  
Lower Bound ◽  
Pattern Complexity ◽  
Infinite Words ◽  
Abelian Equivalence

AbstractIn this paper, we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection. We show that in the case of binary words, the bound is actually achieved and gives a characterization of recurrent aperiodic words.

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