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 - 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/Territory	Italy
City	Taormina
Period	6/20/05 → 6/25/05

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "Generalizations of Cauchy's determinant and Schur's Pfaffian",

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",

year = "2005",

language = "English",

pages = "231--242",

note = "17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 ; Conference date: 20-06-2005 Through 25-06-2005",

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TY - CONF

T1 - Generalizations of Cauchy's determinant and Schur's Pfaffian

AU - Ishikawa, Masao

AU - Okada, Soichi

AU - Tagawa, Hiroyuki

AU - Zeng, Jiang

PY - 2005

Y1 - 2005

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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UR - http://www.scopus.com/inward/citedby.url?scp=84861130054&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:84861130054

SP - 231

EP - 242

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

Y2 - 20 June 2005 through 25 June 2005

ER -

Generalizations of Cauchy's determinant and Schur's Pfaffian

Abstract

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ASJC Scopus subject areas

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