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In 2014, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length $n$ contain $n$ distinct nonempty palindromic factors. In 2020, Currie, Mol, and Rampersad pr
Externí odkaz:
http://arxiv.org/abs/2409.12068
Autor:
Currie, James D., Rampersad, Narad
It is known that there are infinite words over finite alphabets with Abelian repetition threshold arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism (length 13) over
Externí odkaz:
http://arxiv.org/abs/2312.16665
Autor:
Currie, James D., Rampersad, Narad
A $4^-$-power is a non-empty word of the form $XXXX^-$, where $X^-$ is obtained from $X$ by erasing the last letter. A binary word is called {\em faux-bonacci} if it contains no $4^-$-powers, and no factor 11. We show that faux-bonacci words bear the
Externí odkaz:
http://arxiv.org/abs/2311.12962
Autor:
Currie, James, Rampersad, Narad
We find the lexicographically least infinite binary rich word having critical exponent $2+\sqrt{2}/2$
Externí odkaz:
http://arxiv.org/abs/2310.07010
Autor:
Currie, James D.
Good words are binary words avoiding factors 11 and 1001, and patterns 0000 and 00010100. We show that good words bear the same relationship to the period-doubling sequence that overlap-free words bear to the Thue-Morse sequence. We prove an analogue
Externí odkaz:
http://arxiv.org/abs/2303.14539
Autor:
Currie, James, Dvořaková, L'ubomíra, Ochem, Pascal, Opočenská, Daniela, Rampersad, Narad, Shallit, Jeffrey
The complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. We study infinite binary words $\bf w$ that avoid sufficiently large complementary factors; that is, if $x$ is a factor of $\bf w$ then
Externí odkaz:
http://arxiv.org/abs/2209.09598
Autor:
Baranwal, Aseem, Currie, James, Mol, Lucas, Ochem, Pascal, Rampersad, Narad, Shallit, Jeffrey
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 25:2, Combinatorics (September 6, 2023) dmtcs:10063
The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $\textit{antisquare}$ is a nonempty word of the form $x\, \overline{x}$. In this paper, we study infinite binary words that
Externí odkaz:
http://arxiv.org/abs/2209.09223
We study the properties of the ternary infinite word p = 012102101021012101021012 ... , that is, the fixed point of the map h:0->01, 1->21, 2->0. We determine its factor complexity, critical exponent, and prove that it is 2-balanced. We compute its a
Externí odkaz:
http://arxiv.org/abs/2206.01776