5 citations · 9 across the 20 of their papers we have counts for
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Matrix representation of meet-irreducible discrete copulas
Masato Kobayashi
Following Aguiló-Suñer-Torrens (2008), Kolesárová-Mesiar-Mordelová-Sempi (2006) and Mayor-Suñer-Torrens (2005), we continue to develop a theory of matrix representation for discret…
A new refinement of Euler numbers on counting alternating permutations
Masato Kobayashi
At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this artic…
Weighted counting of Bruhat paths by shifted -polynomials
Masato Kobayashi
We revisit -polynomials with introducing the new idea ``shifted -polynomials" (or Bruhat weight) for all Bruhat intervals in finite Coxeter groups. Then, we apply these polyn…
Construction of double coset system of a Coxeter group and its applications to Bruhat graphs
Masato Kobayashi
We develop combinatorics of parabolic double cosets in finite Coxeter groups as a follow-up of recent articles by Billey-Konvalinka-Petersen-Slofstra-Tenner and Petersen. (1) We co…
Weighted counting of inversions on alternating sign matrices
Masato Kobayashi
We extend the author's formula (2011) of weighted counting of inversions on permutations to the one on alternating sign matrices. The proof is based on the sequential construction…
A directed graph structure of alternating sign matrices
Masato Kobayashi
We introduce a new directed graph structure into the set of alternating sign matrices. This includes Bruhat graph (Bruhat order) of the symmetric groups as a subgraph (subposet). D…
Enumerative combinatorics on determinants and signed bigrassmannian polynomials
Masato Kobayashi
As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed big…
Bruhat order and graph structures of lower intervals in Coxeter groups
Masato Kobayashi
We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we…
Inequalities on Bruhat graphs, R- and Kazhdan-Lusztig polynomials
Masato Kobayashi
From a combinatorial perspective, we establish three inequalities on coefficients of - and Kazhdan-Lusztig polynomials for crystallographic Coxeter groups: (1) Nonnegativity of…
Enumeration of bigrassmannian permutations below a permutation in Bruhat order
Masato Kobayashi
In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove for…