13 citations · 16 across the 4 of their papers we have counts for
5 papers
An elliptic generalization of Schur's Pfaffian identity
Soichi Okada
We present a Pfaffian identity involving elliptic functions, whose rational limit gives a generalization of Schur's Pfaffian identity for Pf ((x_j - x_i)/(x_j + x_i)). This identit…
Generalizations of Cauchy's Determinant and Schur's Pfaffian
Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa +1
We present several generalizations of Cauchy's determinant and Schur's Pfaffian by considering matrices whose entries involve some generalized Vandermonde determinants. Special cas…
A Pfaffian-Hafnian analogue of Borchardt's identity
Masao Ishikawa, Hiroyuki Kawamuko, Soichi Okada
We present an identity which can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity. We give a proof using the complex a…
Enumeration of Symmetry Classes of Alternating Sign Matrices and Characters of Classical Groups
Soichi Okada
An alternating sign matrix is a square matrix with entries 1, 0 and -1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate…
The number of rhombus tilings of a "punctured" hexagon and the minor summation formula
Soichi Okada, Christian Krattenthaler
We compute the number of all rhombus tilings of a hexagon with sides , of which the central triangle is removed, provided have the same parity. The resul…