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pro vyhledávání: '"05A05, 05A15"'
Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed $k$-ary tree, where we place $k^\ell$ chips o
Externí odkaz:
http://arxiv.org/abs/2410.23265
It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed first letter are identical when we perform a simple change of the firs
Externí odkaz:
http://arxiv.org/abs/2410.23206
Autor:
Sagan, Bruce E., Wilson, Alexander N.
Let u be a word over the positive integers. Motivated in part by a question from representation theory, we study the centralizer set of u which is C(u) = {w | uw is Knuth-equivalent to wu}. In particular, we give various necessary conditions for w to
Externí odkaz:
http://arxiv.org/abs/2410.20460
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:
Ray, Souvik
In this paper, we shall try to deduce asymptotic behaviour of component spectrum of random $n \times n$ magical squares with line sum $r \in \mathbb{N}$, which can also be identified as $r$-regular bipartite graphs on $2n$ vertices, chosen uniformly
Externí odkaz:
http://arxiv.org/abs/2410.10334
Autor:
Lazar, Alexander, Linusson, Svante
Set-valued standard Young tableaux are a generalization of standard Young tableaux due to Buch (2002) with applications in algebraic geometry. The enumeration of set-valued SYT is significantly more complicated than in the ordinary case, although pro
Externí odkaz:
http://arxiv.org/abs/2410.04860
Motivated by a problem in population genetics, we examine the combinatorics of dissimilarity for pairs of random unordered draws of multiple objects, with replacement, from a collection of distinct objects. Consider two draws of size $K$ taken with r
Externí odkaz:
http://arxiv.org/abs/2410.00221
Autor:
Boualam, Rezig, Ahmia, Moussa
In this paper, we provide criteria for the log-concavity of rows and the strong $q$-log-convexity of the generating functions of rows in more generalized triangles. Additionally, we prove that the bi$^s$nomial transformation not only preserves the st
Externí odkaz:
http://arxiv.org/abs/2409.18886
Autor:
Linusson, Svante, Verkama, Emil
We enumerate the numbers $Av_n^k(1324)$ of 1324-avoiding $n$-permutations with exactly $k$ inversions for all $k$ and $n \geq (k+7)/2$. The result depends on a structural characterization of such permutations in terms of a new notion of almost-decomp
Externí odkaz:
http://arxiv.org/abs/2408.15075
This paper is a continuation of earlier work of Arslan \cite{Ars}, who introduced the Mahonian number of type $B$ by using a new statistic on the hyperoctahedral group $B_{n}$, in response to questions he suggested in his paper entitled "{\it A combi
Externí odkaz:
http://arxiv.org/abs/2408.02424