このエントリーをはてなブックマークに追加
ID 53047
FullText URL
Author
Kobayashi, Masato
Abstract
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 afterward the author developed (2011). Second, bigrassmannian determinant is a q-analog of the determinant with respect to our statistic. It plays a key role for a determinantal expression of those polynomials. We further show that bigrassmannian determinant satisfies weighted condensation as a generalization of Dodgson, Jacobi-Desnanot and Robbins-Rumsey (1986).
Keywords
Bigrassmannian permutations
Bruhat order
Permutation statistics
Robbins-Rumsey determinant
Symmetric Groups
Tournaments
Vandermonde determinant
Published Date
2015-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume57
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
159
End Page
172
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2015 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol57/iss1/10
JaLCDOI