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» A class of combinatorial identities
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COMBINATORICS
2002
76views more  COMBINATORICS 2002»
13 years 6 months ago
On the Number of Distributive Lattices
We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and...
Marcel Erné, Jobst Heitzig, Jürgen Rei...
JCT
2010
93views more  JCT 2010»
13 years 4 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
DM
2006
81views more  DM 2006»
13 years 6 months ago
A combinatorial identity with application to Catalan numbers
By a very simple argument, we prove that if l, m, n {0, 1, 2, . . . } then l k=0 (-1)m-k l k m - k n 2k k - 2l + m = l k=0 l k 2k n n - l m + n - 3k - l . On the basis of this ide...
Hao Pan, Zhi-Wei Sun
JCT
2007
149views more  JCT 2007»
13 years 5 months ago
Weighted forms of Euler's theorem
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan’s “lost” notebook, we obtain weighted forms of Euler’s theorem on part...
William Y. C. Chen, Kathy Q. Ji