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» A Bijective Proof of Borchardt's Identity
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COMBINATORICS
2004
112views more  COMBINATORICS 2004»
9 years 6 months ago
A Bijective Proof of Borchardt's Identity
We prove Borchardt's identity det 1 xi - yj per 1 xi - yj = det 1 (xi - yj)2 by means of sign-reversing involutions.
Dan Singer
COMBINATORICS
2000
96views more  COMBINATORICS 2000»
9 years 6 months ago
Bijections for Hook Pair Identities
Short, bijective proofs of identities for multisets of `hook pairs' (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally foun...
Christian Krattenthaler
DM
2008
88views more  DM 2008»
9 years 7 months ago
Bijective proofs of Gould's and Rothe's identities
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which a...
Victor J. W. Guo
EJC
2010
9 years 5 months ago
A proof of Bressoud's conjecture related to the Rogers-Ramanujan identities
The Rogers-Ramanujan Identities have many natural and significant generalizations. The generalization presented in this note was first studied by D. Bressoud, by considering the...
Shishuo Fu
JCT
2010
93views more  JCT 2010»
9 years 5 months ago
Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions
Combinatorial proofs are given for certain entries in Ramanujan’s lost notebook. Bijections of Sylvester, Franklin, Wright, and Yee are employed. A new bijection, involving the n...
Bruce C. Berndt, Byungchan Kim, Ae Ja Yee
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