2 citations · 3 across the 8 of their papers we have counts for
9 papers
Hook length biases and general linear partition inequalities
Cristina Ballantine, Hannah Burson, William Craig +2
Motivated in part by hook-content formulas for certain restricted partitions in representation theory, we consider the total number of hooks of fixed length in odd versus distinct…
On integer partitions corresponding to numerical semigroups
Hannah E. Burson, Hayan Nam, Simone Sisneros-Thiry
Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. We e…
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…
Mock theta functions and related combinatorics
Cristina Ballantine, Hannah E. Burson, Amanda Folsom +3
In this paper we add to the literature on the combinatorial nature of the mock theta functions, a collection of curious -hypergeometric series introduced by Ramanujan in his las…
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…
On a Partition Identity of Lehmer
Cristina Ballantine, Hannah E. Burson, Amanda Folsom +3
Euler's identity equates the number of partitions of any non-negative integer n into odd parts and the number of partitions of n into distinct parts. Beck conjectured and Andrews p…
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…
A bijective proof of a false theta function identity from Ramanujan's lost notebook
Hannah Burson
In his lost notebook, Ramanujan listed 5 identities related to the false theta function A new combinatorial interpretation and proof…