9 citations · 11 across the 5 of their papers we have counts for
5 papers
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…
Minor summation formula and a proof of Stanley's open problem
Masao Ishikawa
In the open problem session of the FPSAC'03, R.P.Stanley gave an open problem. The purpose of this paper is to give a proof of this open problem. At the end of this paper we presen…
A generalization of Kawanaka's identity for Hall-Littlewood polynomials and applications
M. Ishikawa, F. Jouhet, J. Zeng
An infinite summation formula of Hall-Littlewood polynomials due to Kawanaka is generalized to a finite summation formula, which implies, as applications, twelve multiple q-identit…
Applications of Minor Summation Formula III, Plucker Relations, Lattice Paths and Pfaffian Identities
Masao Ishikawa, Masato Wakayama
The initial purpose of this paper is to provide a combinatorial proof of the minor summation formula of Pfaffians based on the lattice path method. There we related Plücker relatio…