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of 65
pro vyhledávání: '"Pantone, Jay"'
A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and has a trapped endpoint. We show that the generating function enumerating GSAWs on a half-infinite strip of finite height is rational,
Externí odkaz:
http://arxiv.org/abs/2407.18205
Publikováno v:
EPTCS 403, 2024, pp. 96-100
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion and Schmi
Externí odkaz:
http://arxiv.org/abs/2406.16403
We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combina
Externí odkaz:
http://arxiv.org/abs/2312.07716
Autor:
Pantone, Jay
We derive the algebraic generating function for inversion sequences avoiding the patterns $201$ and $210$ by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and then solv
Externí odkaz:
http://arxiv.org/abs/2310.19632
Autor:
Albert, Michael H., Bean, Christian, Claesson, Anders, Nadeau, Émile, Pantone, Jay, Ulfarsson, Henning
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and provide a
Externí odkaz:
http://arxiv.org/abs/2202.07715
Autor:
Bóna, Miklós, Pantone, Jay
We enumerate permutations that avoid all but one of the $k$ patterns of length $k$ starting with a monotone increasing subsequence of length $k-1$. We compare the size of such permutation classes to the size of the class of permutations avoiding the
Externí odkaz:
http://arxiv.org/abs/2103.06918
Worpitzky's identity expresses $n^p$ in terms of the Eulerian numbers and binomial coefficients: $$n^p = \sum_{i=0}^{p-1} \genfrac<>{0pt}{}{p}{i} \binom{n+i}{p}.$$ Pita-Ruiz recently defined numbers $A_{a,b,r}(p,i)$ implicitly to satisfy a generalize
Externí odkaz:
http://arxiv.org/abs/1910.02977
Permutations in the image of the pop-stack operator are said to be pop-stacked. We give a polynomial-time algorithm to count pop-stacked permutations up to a fixed length and we use it to compute the first 1000 terms of the corresponding counting seq
Externí odkaz:
http://arxiv.org/abs/1908.08910
Autor:
Bóna, Miklós, Pantone, Jay
Publikováno v:
In Journal of Symbolic Computation May-June 2023 116:130-138
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