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math.CO2022
On the positivity of infinite products connected to partitions with even parts below odd parts and copartitions
Hannah E. Burson, Dennis Eichhorn
In this paper, we give a combinatorial proof of a positivity result of Chern related to Andrews's -type partitions. This combinatorial proof comes after reframing C…
math.CO2021
Copartitions
Hannah E. Burson, Dennis Eichhorn
We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions…
math.CO2019
Refined counting of core partitions into -distinct parts
Hannah E. Burson, Simone Sisneros-Thiry, Armin Straub
Using a combinatorial bijection with certain abaci diagrams, Nath and Sellers have enumerated -core partitions into distinct parts. We generalize their result in se…