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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.CO2018
A tiling proof of Euler's pentagnal number theorem and generalizations
Dennis Eichhorn, Hayan Nam, Jaebum Sohn
In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider various s…