4 citations · 13 across the 35 of their papers we have counts for
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Generalizations of POD and PED partitions
Cristina Ballantine, Amanda Welch
Partitions with even (respectively odd) parts distinct and all other parts unrestricted are often referred to as PED (respectively POD) partitions. In this article, we generalize t…
PED and POD partitions: combinatorial proofs of recurrence relations
Cristina Ballantine, Amanda Welch
PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca…
Combinatorial proofs of theorems of Merca on the sum of different parts congruent to modulo in all partitions of
Cristina Ballantine
We give combinatorial proofs of several recent results due to Merca on the sum of different parts congruent to modulo in all partitions of . The proofs make use of some…
Partitions enumerated by self-similar sequences
Cristina Ballantine, George Beck
The Fibonacci numbers are the prototypical example of a recursive sequence, but grow too quickly to enumerate sets of integer partitions. The same is true for the other classical s…
On the number of parts in all partitions enumerated by the Rogers-Ramanujan identities
Cristina Ballantine, Amanda Folsom
The celebrated Rogers-Ramanujan identities equate the number of integer partitions of () with parts congruent to (respectively $\pm 2 \pmod{5}…
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…