7 papers
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…
On the parity of the number of -copartitions of
Hannah E. Burson, Dennis Eichhorn
We continue the study of the -copartition function , which arose as a combinatorial generalization of Andrews' partitions with even parts below odd…
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…
Hybrid Proofs of the -Binomial Theorem and other identities
Dennis Eichhorn, James Mc Laughlin, Andrew V. Sills
We give "hybrid" proofs of the -binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the…
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…
Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts
Felix Breuer, Dennis Eichhorn, Brandt Kronholm
In this paper, we use a branch of polyhedral geometry, Ehrhart theory, to expand our combinatorial understanding of congruences for partition functions. Ehrhart theory allows us to…