Generalizations of Cauchy's determinant and Schur's Pfaffian

Masao Ishikawa; Soichi Okada; Hiroyuki Tagawa; Jiang Zeng

Generalizations of Cauchy's determinant and Schur's Pfaffian

Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to conference › Paper › peer-review

Abstract

We present several generalizations of Cauchy's determinant det (1=(x _i + y _j)) and Schur's Pfaffian Pf ((x _j - x _i)=(x _j + x _i)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood- Richardson coefficients involving a rectangular partition.

Original language	English
Pages	231-242
Number of pages	12
Publication status	Published - Dec 1 2005
Externally published	Yes
Event	17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy Duration: Jun 20 2005 → Jun 25 2005

Other

Other	17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
Country	Italy
City	Taormina
Period	6/20/05 → 6/25/05

ASJC Scopus subject areas

Algebra and Number Theory

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abstract = "We present several generalizations of Cauchy's determinant det (1=(x i + y j)) and Schur's Pfaffian Pf ((x j - x i)=(x j + x i)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood- Richardson coefficients involving a rectangular partition.",

author = "Masao Ishikawa and Soichi Okada and Hiroyuki Tagawa and Jiang Zeng",

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AU - Ishikawa, Masao

AU - Okada, Soichi

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

PY - 2005/12/1

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N2 - We present several generalizations of Cauchy's determinant det (1=(x i + y j)) and Schur's Pfaffian Pf ((x j - x i)=(x j + x i)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood- Richardson coefficients involving a rectangular partition.

AB - We present several generalizations of Cauchy's determinant det (1=(x i + y j)) and Schur's Pfaffian Pf ((x j - x i)=(x j + x i)) by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previous formulae due to S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood- Richardson coefficients involving a rectangular partition.

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T2 - 17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05

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