2 citations · 2 across the 5 of their papers we have counts for
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Notes for Neighborly Partitions
Kathleen O'Hara, Dennis Stanton
A proof of the first Rogers-Ramanujan identity is given using admissible neighborly partitions. This completes a program initiated by Mohsen and Mourtada. The admissible neighborly…
On q-integrals over order polytopes
Jang Soo Kim, Dennis Stanton
A combinatorial study of multiple -integrals is developed. This includes a -volume of a convex polytope, which depends upon the order of -integration. A multiple -integ…
Binomial Andrews-Gordon-Bressoud identities
Dennis Stanton
Binomial versions of the Andrews-Gordon-Bressoud identities are given.
The Combinatorics of Associated Laguerre Polynomials
Jang Soo Kim, Dennis Stanton
The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation table…
Refinements of the Rogers-Ramanujan identities
Kathleen O'Hara, Dennis Stanton
Refinements of the classical Rogers-Ramanujan identities are given in which some parts are weighted. Combinatorial interpretations refining MacMahon's results are corollaries.