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ID 53047
フルテキストURL
著者
Kobayashi, Masato Graduate School of Science and Engineering Department of Mathematics Saitama University
抄録
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).
キーワード
Bigrassmannian permutations
Bruhat order
Permutation statistics
Robbins-Rumsey determinant
Symmetric Groups
Tournaments
Vandermonde determinant
発行日
2015-01
出版物タイトル
Mathematical Journal of Okayama University
57巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
159
終了ページ
172
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
言語
English
著作権者
Copyright©2015 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol57/iss1/10
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