48 citations · 60 across the 17 of their papers we have counts for
11 papers · 1 filter
Small palindromic lengths in free groups and word equations with antimorphisms
Anna E. Frid
The palindromic length of a finite word is defined as the minimal number of palindromes such that their product is . Clearly, this function may take different values dependi…
Prefix palindromic length of the Sierpinski word
Dora V. Bulgakova, Anna E. Frid, Jérémy Scanvic
The prefix palindromic length of an infinite word is the minimal number of concatenated palindromes needed to express the prefix of length of $…
The number of valid factorizations of Fibonacci prefixes
Pierre Bonardo, Anna E. Frid, Jeffrey Shallit
We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strict…
Cost and dimension of words of zero topological entropy
Julien Cassaigne, Anna E. Frid, Svetlana Puzynina +1
Let denote the free monoid generated by a finite nonempty set In this paper we introduce a new measure of complexity of languages defined in terms of th…
Words containing all permutations of a family of factors
Anna E. Frid
We prove that if a uniformly recurrent infinite word contains as a factor any finite permutation of words from an infinite family, then either this word is periodic, or its complex…
Minimal complexity of equidistributed infinite permutations
Sergey V. Avgustinovich, Anna E. Frid, Svetlana Puzynina
An infinite permutation is a linear ordering of the set of natural numbers. An infinite permutation can be defined by a sequence of real numbers where only the order of elements is…
The number of binary rotation words
Anna E. Frid, Damien Jamet
We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the…
On minimal factorizations of words as products of palindromes
Anna E. Frid, Svetlana Puzynina, Luca Zamboni
Given a finite word u, we define its palindromic length |u|_{pal} to be the least number n such that u=v_1v_2... v_n with each v_i a palindrome. We address the following open quest…
On possible growth of Toeplitz languages
Julien Cassaigne, Anna Frid, Fedor Petrov
We consider a new family of factorial languages whose subword complexity grows as , where is the root of some transcendent equation. Analytical methods and in particula…
Infinite permutations of lowest maximal pattern complexity
S. V. Avgustinovich, A. E. Frid, T. Kamae +1
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some…
On the number of factors in codings of three interval exchange
Petr Ambrož, Anna Frid, Zuzana Masáková +1
We consider exchange of three intervals with permutation . The aim of this paper is to count the cardinality of the set $3\iet(N)$ of all words of length which appear…