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pro vyhledávání: '"Shur, Arseny M."'
We revisit the topic of power-free morphisms, focusing on the properties of the class of complementary morphisms. Such morphisms are defined over a $2$-letter alphabet, and map the letters 0 and 1 to complementary words. We prove that every prefix of
Externí odkaz:
http://arxiv.org/abs/2310.15064
Autor:
Shur, Arseny M., Rubinchik, Mikhail
For an arbitrary finite family of graphs, the distance labeling problem asks to assign labels to all nodes of every graph in the family in a way that allows one to recover the distance between any two nodes of any graph from their labels. The main go
Externí odkaz:
http://arxiv.org/abs/2308.15242
We study the threshold between avoidable and unavoidable repetitions in infinite balanced sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and Vandomme says that the minimal critical exponent of balanced sequences over the
Externí odkaz:
http://arxiv.org/abs/2112.02854
Autor:
Petrova, Elena A., Shur, Arseny M.
Abelian repetition threshold ART(k) is the number separating fractional Abelian powers which are avoidable and unavoidable over the k-letter alphabet. The exact values of ART(k) are unknown; the lower bounds were proved in [A.V. Samsonov, A.M. Shur.
Externí odkaz:
http://arxiv.org/abs/2109.09306
Autor:
Petrova, Elena A., Shur, Arseny M.
We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language and to the
Externí odkaz:
http://arxiv.org/abs/2105.02750
Autor:
Rubinchik, Mikhail, Shur, Arseny M.
Given a string $s$ of length $n$ over a general alphabet and an integer $k$, the problem is to decide whether $s$ is a concatenation of $k$ nonempty palindromes. Two previously known solutions for this problem work in time $O(kn)$ and $O(n\log n)$ re
Externí odkaz:
http://arxiv.org/abs/2002.03965
Akademický článek
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Autor:
Petrova, Elena A., Shur, Arseny M.
We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to th
Externí odkaz:
http://arxiv.org/abs/1812.11119
Autor:
Shallit, Jeffrey, Shur, Arseny M.
We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that -- the Thue-Morse word has the minimum possible subword complexity over all overlap-free binary word
Externí odkaz:
http://arxiv.org/abs/1801.05376