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The prefix palindromic length $p_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. This function is surprisingly difficult to study; in part
Externí odkaz:
http://arxiv.org/abs/2201.09556
The prefix palindromic length $\mathrm{PPL}_{\mathbf{u}}(n)$ of an infinite word $\mathbf{u}$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $\mathbf{u}$. Since 2013, it is still unknown if $\mathrm{PP
Externí odkaz:
http://arxiv.org/abs/2009.02934
Autor:
Frid, Anna E.
Publikováno v:
Journal of Integer Sequences, Vol. 22 (2019), Article 19.7.8
The prefix palindromic length $PPL_u(n)$ of an infinite word $u$ is the minimal number of concatenated palindromes needed to express the prefix of length $n$ of $u$. In a 2013 paper with Puzynina and Zamboni we stated the conjecture that $PPL_u(n)$ i
Externí odkaz:
http://arxiv.org/abs/1906.09392
Autor:
Andrieu, Mélodie, Frid, Anna E.
The problem we consider is the following: Given an infinite word $w$ on an ordered alphabet, construct the sequence $\nu_w=(\nu[n])_n$, equidistributed on $[0,1]$ and such that $\nu[m]<\nu[n]$ if and only if $\sigma^m(w)<\sigma^n(w)$, where $\sigma$
Externí odkaz:
http://arxiv.org/abs/1807.08321
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 strictly) decreasing sequence of standard Fibonacci words. In particular, we
Externí odkaz:
http://arxiv.org/abs/1806.09534
Publikováno v:
In Theoretical Computer Science 4 November 2021 891:13-23
Let $A^*$ denote the free monoid generated by a finite nonempty set $A.$ In this paper we introduce a new measure of complexity of languages $L\subseteq A^*$ defined in terms of the semigroup structure on $A^*.$ For each $L\subseteq A^*,$ we define i
Externí odkaz:
http://arxiv.org/abs/1607.04728
Autor:
Frid, Anna E.
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 complexity (that is, the number of factors) grows faster than linearly. This
Externí odkaz:
http://arxiv.org/abs/1510.08114
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 taken into account. In the paper we investigate a new class of {\it e
Externí odkaz:
http://arxiv.org/abs/1503.06188
Autor:
Frid, Anna E., Jamet, Damien
Publikováno v:
RAIRO-Theor. Inf. Appl. 48 (2014) 453-465
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 precise asymptotics for it, which happens to be O(n^4). The result con
Externí odkaz:
http://arxiv.org/abs/1302.3722