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pro vyhledávání: '"68R15"'
Autor:
Nowotka, Dirk, Wiedenhöft, Max
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of variables by a
Externí odkaz:
http://arxiv.org/abs/2411.07275
Autor:
Nowotka, Dirk, Wiedenhöft, Max
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of variables by as
Externí odkaz:
http://arxiv.org/abs/2411.06904
Autor:
Kohen, Nadav
We give a formula for the density of $0$ in the sequence of generalized Motzkin numbers, $M^{a,b}_n$, modulo a prime, $p$, in terms of the first $p$ generalized central trinomial coefficients $T^{a,b}_n\mod p$ (with $n
Externí odkaz:
http://arxiv.org/abs/2411.03681
Autor:
Allaart, Pieter, Kong, Derong
Given $\beta>1$, let $T_\beta$ be the $\beta$-transformation on the unit circle $[0,1)$, defined by $T_\beta(x)=\beta x\pmod 1$. For each $t\in[0,1)$ let $K_\beta(t)$ be the survivor set consisting of all $x\in[0,1)$ whose orbit $\{T^n_\beta(x): n\ge
Externí odkaz:
http://arxiv.org/abs/2411.03516
Periodic orbits (equivalence classes of closed cycles up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra of quant
Externí odkaz:
http://arxiv.org/abs/2410.23417
Autor:
Zhao, William
We introduce the stack-sorting map $\text{SC}_\sigma$ that sorts, in a right-greedy manner, an input permutation through a stack that avoids some vincular pattern $\sigma$. The stack-sorting maps of Cerbai et al. in which the stack avoids a pattern c
Externí odkaz:
http://arxiv.org/abs/2410.17057
Autor:
Mercaş, Robert, Teh, Wen Chean
The focus of this work is the study of Parikh matrices with emphasis on two concrete problems. In the first part of our presentation we show that a conjecture by Dick at al. in 2021 only stands in the case of ternary alphabets, while providing counte
Externí odkaz:
http://arxiv.org/abs/2410.15004
Autor:
Yoshida, Yuuya
Solov'ev (1966), Nielsen (1973), and Blom (1982) independently showed a formula for the expected waiting time until a given finite pattern first occurs in random data. In this paper, we give a simple and combinatorial proof of the formula.
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Externí odkaz:
http://arxiv.org/abs/2410.13426
Autor:
Rukavicka, Josef
The palindromic length of the finite word $v$ is equal to the minimal number of palindromes whose concatenation is equal to $v$. It was conjectured in 2013 that for every infinite aperiodic word $x$, the palindromic length of its factors is not bound
Externí odkaz:
http://arxiv.org/abs/2410.12714
Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of pseudorandom
Externí odkaz:
http://arxiv.org/abs/2410.12534