A Pfaffian-Hafnian analogue of Borchardt's identity

Electronic Journal of Combinatorics

Volumn 12, Issue 1 N, 2005, Pages

  Ishikawa, Masao ^a   Kawamuko, Hiroyuki ^b   Okada, Soichi ^c  

^a TOTTORI UNIVERSITY   (Japan)

^b MIE UNIVERSITY   (Japan)

^c NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21244456491     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. C. W. Borchardt, Bestimmung der symmetrischen Verbindungen vermittelst ihrer erzeugenden Funktion, J. Reine Angew. Math. 53 (1855), 193-198.
2. A. L. Cauchy, Mémoire sur les fonctions altertées et sur les sommes alternées, Exercices Anal, et Phys. Math. 2 (1841), 151-159.
3. L. Carlitz and J. Levine, An identity of Cayley, Amer. Math. Monthly 67 (1960), 571-573.
4. M. Ishikawa, S. Okada and M. Wakayama, Applications of minor summation formulas I: Littlewood's formulas, J. Algebra 183 (1996), 193-216.
5. M. Ishikawa and M. Wakayama, Applications of minor summation formulas II: Pfaffians and Schur polynomials, J. Combin. Theory Ser. A 88 (1999), 136-157.
6. M. Ishikawa and M. Wakayama, Applications of minor summation formulas III: Plücker relations, lattice paths and Pfaffian identities, arXiv:math.CO/0312358, to appear in J. Combin. Theory Ser. A.
7. D. Knuth, Overlapping Pfaffians, Electron. J. Combin. 3 (2) ("The Foata Festschrift") (1996), 151-163.
8. C. Krattenthaler, Advanced determinant calculus, Sem. Lothar. Combin. 42 ("The Andrews Festschrift") (1999), Article B42q.
9. D. Laksov, A. Lascoux and A. Thorup, On Giambelli's theorem on complete correlations, Acta Math. 162 (1989), 143-199.
10. S. Okada, Application of minor summation formulas to rectangular-shaped representations of classical groups, J. Algebra 205 (1998), 337-367.
11. S. Okada, Enumeration of symmetry classes of alternating sign matrices and characters of classical groups, arXiv:math.CO/0408234, to appear.
12. I. Schur, Über die Darstellung der symmetrischen und der alternirenden Gruppe durch gebrochene lineare Substitutuionen, J. Reine Angew. Math. 139 (1911), 155-250.
13. D. Singer, A bijective proof of Borchardt's identity, Electron. J. Combin. 11 (1), R48
14. J. R. Stembridge, Non-intersecting paths, Pfaffians and plane partitions, Adv. Math. 83 (1990), 96-131.