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math.CO2004
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…
math.CO2004★ 9 cited
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…
math.CO2004★ 2 cited
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…