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The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with critical exp
Externí odkaz:
http://arxiv.org/abs/2406.06513
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:
Narcia-Macias, Christian I., Guardado, Joselito, Rodriguez, Jocell, Rampersad-Ammons, Joanne, Enriquez, Erik, Kim, Dong-Chul
Utilizing computer vision and the latest technological advancements, in this study, we developed a honey bee monitoring system that aims to enhance our understanding of Colony Collapse Disorder, honey bee behavior, population decline, and overall hiv
Externí odkaz:
http://arxiv.org/abs/2309.08955
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:
Raunak M. Nair, MD, Sanchit Chawla, MD, Feras Alkhalaileh, MD, Bahaa Abdelghaffar, MD, Agam Bansal, MD, Andrew Higgins, MD, Ran Lee, MD, Penelope Rampersad, MD, Umesh.N. Khot, MD, Wael A. Jaber, MD, Grant W. Reed, MD, Paul C. Cremer, MD, Venu Menon, MD
Publikováno v:
JACC: Advances, Vol 3, Iss 11, Pp 101303- (2024)
Background: The clinical characteristics and outcomes of patients who develop cardiogenic shock (CS) secondary to primary valvular dysfunction (valvular cardiogenic shock [VCS]) remain unclear. Objectives: The purpose of this study was to describe th
Externí odkaz:
https://doaj.org/article/7180b6fa0f3d4e70b7753f0197204b5c
