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pro vyhledávání: '"Rampersad, Narad"'
Autor:
Rampersad, Narad
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G1, Pp 323-330 (2023)
The Fibonacci word $\mathbf{f} = 010010100100101\cdots $ is one of the most well-studied words in the area of combinatorics on words. It is not periodic, but nevertheless contains many highly periodic factors (contiguous subwords). For example, it co
Externí odkaz:
https://doaj.org/article/85b9e64149e7448197b5d37a7e1b66a7
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:
Rampersad, Narad, Wiebe, Max
If $u$ and $v$ are two words, the correlation of $u$ over $v$ is a binary word that encodes all possible overlaps between $u$ and $v$. This concept was introduced by Guibas and Odlyzko as a key element of their method for enumerating the number of wo
Externí odkaz:
http://arxiv.org/abs/2309.07070
Autor:
Rampersad, Narad, Wiebe, Max
Wu showed that certain sums of products of binomial coefficients modulo 2 are given by the run length transforms of several famous linear recurrence sequences, such as the positive integers, the Fibonacci numbers, the extended Lucas numbers, and Nara
Externí odkaz:
http://arxiv.org/abs/2309.04012
Autor:
Rampersad, Narad, Shallit, Jeffrey
We show how to obtain, via a unified framework provided by logic and automata theory, many classical results of Brillhart and Morton on Rudin-Shapiro sums. The techniques also facilitate easy proofs for new results.
Comment: This is the full ver
Comment: This is the full ver
Externí odkaz:
http://arxiv.org/abs/2302.00405
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 2 (Special issue: Numeration, Liège 2023, dedicated to the 75th birthday of professor Christiane Frougny) (August 2, 2024) cm:12695
We study various aspects of Dyck words appearing in binary sequences, where $0$ is treated as a left parenthesis and $1$ as a right parenthesis. We show that binary words that are $7/3$-power-free have bounded nesting level, but this no longer holds
Externí odkaz:
http://arxiv.org/abs/2301.06145
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