Results 21 to 30 of about 74,505 (227)
Enumerative combinatorics on determinants and signed bigrassmannian polynomials
, 2019 As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed bigrassmannian polynomial is a variant of the statistic given by the number of bigrassmannian permutations below a permutation in Bruhat order as Reading suggested (2002) and ...
Masato Kobayashi
openalex +5 more sources
Book Review: Enumerative combinatorics, Volume 2 [PDF]
Bulletin of the American Mathematical Society, 2001 Ira M. Gessel
openalex +3 more sources
THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G [PDF]
Journal of Algebraic Systems, 2020 To a simple graph $G=(V,E)$, we correspond a simple graph $G_{\triangle,\square}$ whose vertex set is $\{\{x,y\}: x,y\in V\}$ and two vertices $\{x,y\},\{z,w\}\in G_{\triangle,\square}$ are adjacent if and only if $\{x,z\},\{x,w\},\{y,z\},\{y,w\}\in V ...
Gh. A. Nasiriboroujeni +2 more
doaj +1 more source
Book Review: Enumerative combinatorics, vol. I [PDF]
Bulletin of the American Mathematical Society, 1987 George E. Andrews
openalex +4 more sources
Enumeration of Graded (3 + 1)-Avoiding Posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The notion of (3+1)-avoidance appears in many places in enumerative combinatorics, but the natural goal of enumerating all (3+1)-avoiding posets remains open. In this paper, we enumerate \emphgraded (3+1)-avoiding posets.
Joel Lewis Brewster, Yan X Zhang
doaj +1 more source
Note on r-central Lah numbers and r-central Lah-Bell numbers
AIMS Mathematics, 2022 The r-Lah numbers generalize the Lah numbers to the r-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The r-Lah number counts the number of partitions
Hye Kyung Kim
doaj +1 more source
Combinatorial reciprocity for non-intersecting paths [PDF]
Enumerative Combinatorics and Applications, 3(2), 2023, 2023 We prove a combinatorial reciprocity theorem for the enumeration of non-intersecting paths in a linearly growing sequence of acyclic planar networks. We explain two applications of this theorem: reciprocity for fans of bounded Dyck paths, and reciprocity for Schur function evaluations with repeated values.
arxiv +1 more source
Enumerative Combinatorics of Intervals in the Dyck Pattern Poset [PDF]
Order, 2021 AbstractWe initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some specific intervals, as well as the number of their covering relations. In most of the cases, we are also able to refine our formulas by rank.
Matteo Cervetti +4 more
openaire +5 more sources
Total positivity for cominuscule Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper we explore the combinatorics of the non-negative part $(G/P)_{\geq 0}$ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams ― certain fillings of generalized Young diagrams which are in bijection with the cells of
Thomas Lam, Lauren Williams
doaj +1 more source
Congruence for Lattice Path Models with Filter Restrictions and Long Steps
Mathematics, 2022 We derive a path counting formula for a two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves the problem of finding an explicit formula for
Dmitry Solovyev
doaj +1 more source