miou_057_159_172.pdf 152 KB
Kobayashi, Masato Graduate School of Science and Engineering Department of Mathematics Saitama University
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).
Mathematical Journal of Okayama University
Department of Mathematics, Faculty of Science, Okayama University
Copyright©2015 by the Editorial Board of Mathematical Journal of Okayama University