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
|
巻 | 57巻
|
号 | 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 |
英語
|
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
|
JaLCDOI |