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A factorisation $x = u_1 u_2 \cdots$ of an infinite word $x$ on alphabet $X$ is called `monochromatic', for a given colouring of the finite words $X^*$ on alphabet $X$, if each $u_i$ is the same colour. Wojcik and Zamboni proved that the word $x$ is
Externí odkaz:
http://arxiv.org/abs/2010.09081
Autor:
Salo, Ville, Törmä, Ilkka
In this short article, we study factor colorings of aperiodic linearly recurrent infinite words. We show that there always exists a coloring which does not admit a monochromatic factorization of the word into factors of increasing lengths.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/1504.05821
In this paper we consider the following question in the spirit of Ramsey theory: Given $x\in A^\omega,$ where $A$ is a finite non-empty set, does there exist a finite coloring of the non-empty factors of $x$ with the property that no factorization of
Externí odkaz:
http://arxiv.org/abs/1307.2828
Autor:
Barge, Marcy
We consider the structure of Pisot substitution tiling spaces, in particular, the structure of those spaces for which the translation action does not have pure discrete spectrum. Such a space is always a measurable m-to-one cover of an action by tran
Externí odkaz:
http://arxiv.org/abs/1301.7094
Autor:
Barge, Marcy, Zamboni, Luca Q.
In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from topological
Externí odkaz:
http://arxiv.org/abs/1301.5745
A subset $A$ of $\nats$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\in \nats} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological dynamics, c
Externí odkaz:
http://arxiv.org/abs/1301.5115
In this paper we study some additive properties of subsets of the set $\nats$ of positive integers: A subset $A$ of $\nats$ is called {\it $k$-summable} (where $k\in\ben$) if $A$ contains $\textstyle \big{\sum_{n\in F}x_n | \emp\neq F\subseteq {1,2,.
Externí odkaz:
http://arxiv.org/abs/1301.5118
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 question: Does there exist an infinite non ultimately periodic word w and a
Externí odkaz:
http://arxiv.org/abs/1210.6179
A subset $A$ of $\mathbb{N}$ is called an IP-set if $A$ contains all finite sums of distinct terms of some infinite sequence $(x_n)_{n\in \mathbb{N}} $ of natural numbers. Central sets, first introduced by Furstenberg using notions from topological d
Externí odkaz:
http://arxiv.org/abs/1110.4225
A factorisation $x = u_1 u_2 \cdots$ of an infinite word $x$ on alphabet $X$ is called `monochromatic', for a given colouring of the finite words $X^*$ on alphabet $X$, if each $u_i$ is the same colour. Wojcik and Zamboni proved that the word $x$ is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89d3f2c850b2d4b0c1f154f0c82fbfd2
http://arxiv.org/abs/2010.09081
http://arxiv.org/abs/2010.09081