Zobrazeno 1 - 10
of 3 177
pro vyhledávání: '"05a05"'
We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fractions with coefficients that are quasi-affine of period 2. Our proofs are
Externí odkaz:
http://arxiv.org/abs/2412.10214
Autor:
Hohlweg, Christophe, Pons, Viviane
In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the left invers
Externí odkaz:
http://arxiv.org/abs/2412.09227
Hertzsprung patterns, recently introduced by Anders Claesson, are subsequences of a permutation contiguous in both positions and values, and can be seen as a subclass of bivincular patterns. This paper investigates Hertzsprung patterns within involut
Externí odkaz:
http://arxiv.org/abs/2412.03449
Autor:
Elizalde, Sergi, Luo, Amya
Nonnesting permutations are permutations of the multiset $\{1,1,2,2,\dots,n,n\}$ that avoid subsequences of the form $abba$ for any $a\neq b$. These permutations have recently been studied in connection to noncrossing (also called quasi-Stirling) per
Externí odkaz:
http://arxiv.org/abs/2412.00336
Autor:
Gao, Jeffrey, Kainen, Paul C.
A permutation of the elements of a graph is a {\it construction sequence} if no edge is listed before either of its endpoints. The complexity of such a sequence is investigated by finding the delay in placing the edges, an {\it opportunity cost} for
Externí odkaz:
http://arxiv.org/abs/2412.00212
Autor:
Goertz, Madeleine, Williams, Aaron
We investigate solutions to the new "Ziggu" family of exponential puzzles. These puzzles have $p$ pieces that form $m$ mazes. We encode the puzzle state as an quaternary number (base $4$) with $n=m+1$ digits, where each digit gives the horizontal or
Externí odkaz:
http://arxiv.org/abs/2411.19291
Autor:
Li, Dan, Zhang, Philip B.
Br\"{a}nd\'{e}n and Claesson introduced the concept of mesh patterns in 2011, and since then, these patterns have attracted significant attention in the literature. Subsequently, in 2015, Hilmarsson \emph{et al.} initiated the first systematic study
Externí odkaz:
http://arxiv.org/abs/2411.18131
Autor:
Pudwell, Lara
We consider a 2-player permutation game inspired by the celebrated Erd\H{o}s-Szekeres Theorem. The game depends on two positive integer parameters $a$ and $b$ and we determine the winner and give a winning strategy when $a \geq b$ and $b \in \left\{2
Externí odkaz:
http://arxiv.org/abs/2411.17875
We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the number of
Externí odkaz:
http://arxiv.org/abs/2411.17812
Autor:
Ulfarsson, Henning
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting functions in ana
Externí odkaz:
http://arxiv.org/abs/2411.17778