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Abstract: We review several determinant and Pfa#an identities, which generalize the evaluation formulae of Cauchy's determinant det (1/(x i + y j )) and Schur's Pfa#an Pf ((x j x i )/(x j + x i )). As a multi-variable generalization, we consider Cauchytype determinants and Schur-type Pfa#ans of matrices with entries involving some generalized Vandermonde determinants. Also we give an elliptic generalization of Schur's Pfa#an identity, which is a Pfa#an counterpart of Frobenius' identity. 1 (Update)
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BibTeX entry: (Update)
@misc{ okada-generalizations,
author = "Soichi Okada",
title = "Generalizations of Cauchy's Determinant Identity and Schur's Pfaffian Identity",
url = "citeseer.ist.psu.edu/753932.html" }
Citations (may not include all citations):161 A Course of Modern Analysis (context) - Whittaker, Watson - 1927
22 Uber die Darstellung der symmetrischen und der alternirenden.. (context) - Schur - 1911
20 Advanced determinant calculus - Krattenthaler - 1999
14 Applications of minor-summation formulas to rectangular-shap.. (context) - Okada - 1998
13 Proofs and Confirmations : The Story of the Alternating Sign.. (context) - Bressoud - 1999
7 On Giambelli's theorem on complete correlations (context) - Laksov, Lascoux et al. - 1989
5 Bestimmung der symmetrischen Verbindungen vermittelst ihrer .. (context) - Borchardt
5 ans and plane partitions (context) - Stembridge, paths - 1990
4 Transformations of elliptic hypergeometric integrals (context) - Rains
3 The Foata Festschrift (context) - Knuth, Pfa et al. - 1996
2 Advanced determinant calculus : a complement (context) - Krattenthaler
2 An elliptic generalization of Schur's Pfa#an identity (context) - Okada
1 Hafnian Analogue of the Borchardt's Identity (context) - Ishikawa, Kawamuko et al.
1 Minor summation formulas of Pfa#ans (context) - Ishikawa, Wakayama - 1995
1 presented at International Conference on Formal Power Series.. (context) - Stanley, problem - 2003
1 Applications of the minor summation formula III: Plucker rel.. (context) - Ishikawa, Wakayama
1 Symmetric Functions and Combinatorial Operators on Polynomia.. (context) - Lascoux - 2003
1 Memoire sur les fonctions altertees et sur les sommes altern.. (context) - Cauchy
1 Multiple elliptic hypergeometric series : an approach from t.. (context) - Kajiwara, Noumi - 2003
1 Symmetric Functions and Hall Polynomials (2nd ed (context) - Macdonald - 1995
1 Two variable Pfa#an identities and symmetric functions (context) - Sundquist - 1996
1 Uber die elliptischen Funktionen zweiter Art (context) - Frobenius
1 Zeng Generalizations of Cauchy's determinant and Schur's Pfa (context) - Ishikawa, Okada et al.
1 Enumeration of symmetry classes of alternating sign matrices.. (context) - Okada
1 Determinant and Pfa#an formulae of Cauchy type and their app.. (context) - Okada - 2004
1 Minor summation formula and a proof of Stanley's open proble.. (context) - Ishikawa
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