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math.CO2023
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…
math.CO2018
Marking and shifting a part in partition theorems
Kathleen O'Hara, Dennis Stanton
Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers-Ramanujan identities, the Gollnitz-Gordon identiti…
math.CO2014
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.