Zobrazeno 1 - 10
of 996
pro vyhledávání: '"Mansour Toufik"'
One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010), 2921--2966), we pro
Externí odkaz:
http://arxiv.org/abs/2406.06365
Autor:
Mansour, Toufik, Shattuck, Mark
Let $\mathcal{C}_n$ denote the set of words $w=w_1\cdots w_n$ on the alphabet of positive integers satisfying $w_{i+1}\leq w_i+1$ for $1 \leq i \leq n-1$ with $w_1=1$. The members of $\mathcal{C}_n$ are known as Catalan words and are enumerated by th
Externí odkaz:
http://arxiv.org/abs/2405.12435
Autor:
Fried, Sela, Mansour, Toufik
Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers $r$ and $s$, this statistic counts the number of occurrences of a rectangle of size $r\times s$ in the ba
Externí odkaz:
http://arxiv.org/abs/2405.06962
We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered grammars associated with the Eulerian polynomials and the second-order Eul
Externí odkaz:
http://arxiv.org/abs/2404.15119
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and generalizatio
Externí odkaz:
http://arxiv.org/abs/2401.06662
Autor:
Fried, Sela, Mansour, Toufik
Generalizing the notion of staircase words, introduced by Knopfmacher et.\ al, we define staircase graph words. These are functions $w$ from the vertex set $V$ of a graph into the set $\{1,2,\ldots,k\}$, such that $|w(x)-w(y)|\leq 1$, for every adjac
Externí odkaz:
http://arxiv.org/abs/2312.08273
Autor:
Fried, Sela, Mansour, Toufik
We obtain an explicit formula for the total number of descents and levels in tensor words and cyclic tensor words of arbitrary dimension. We also establish the exact maximal number of descents in words and use it to obtain an upper bound on the maxim
Externí odkaz:
http://arxiv.org/abs/2311.11324
Publikováno v:
Open Mathematics, Vol 14, Iss 1, Pp 908-912 (2016)
In this paper, we present differential equation for the generating function of the p, q-Touchard polynomials. An application to ordered partitions of a set is investigated.
Externí odkaz:
https://doaj.org/article/5d74f91ef9c1468ead850a13ce07e3d4
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:1, Permutation Patterns 2023, Special issues (August 21, 2024) dmtcs:12273
In this paper, we study pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingr\'imsson (2011) for ascent sequences. More precisely, we provide systematic
Externí odkaz:
http://arxiv.org/abs/2309.06518
Autor:
Fried, Sela, Mansour, Toufik
Let $p_n$ be the maximal sum of the entries of $A^2$, where $A$ is a square matrix of size $n$, consisting of the numbers $1,2,\ldots,n^2$, each appearing exactly once. We prove that $m_n=\Theta(n^7)$. More precisely, we show that $n(240n^{6}+28n^{5}
Externí odkaz:
http://arxiv.org/abs/2308.00348