6 citations · 11 across the 7 of their papers we have counts for
9 papers
Combinatorial proofs of inequalities involving the number of partitions with parts separated by parity
Cristina Ballantine, Amanda Welch
We consider the number of various partitions of with parts separated by parity and prove combinatorially several inequalities between these numbers. For example, we show that f…
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…
Toggling, rowmotion, and homomesy on interval-closed sets
Jennifer Elder, Nadia Lafrenière, Erin McNicholas +2
Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of interval-closed sets of finite posets from enumerative and dynamical perspectives.…
Homomesies on permutations -- an analysis of maps and statistics in the FindStat database
Jennifer Elder, Nadia Lafrenière, Erin McNicholas +2
In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. H…
Beck-type companion identities for Franklin's identity
Cristina Ballantine, Amanda Welch
The original Beck conjecture, now a theorem due to Andrews, states that the difference in the number of parts in all partitions into odd parts and the number of parts in all strict…
Beck-type identities: new combinatorial proofs and a theorem for parts congruent to mod
Cristina Ballantine, Amanda Welch
Let be the set of -regular partitions of , the set of partitions of with parts repeated at most times, the…
Beck-type identities for Euler pairs of order
Cristina Ballantine, Amanda Welch
Partition identities are often statements asserting that the set of partitions of subject to condition is equinumerous to the set of partition…
Double Affine Bruhat Order
Amanda Welch
We classify cocovers and covers of a given element of the double affine Weyl semigroup W with respect to the Bruhat order, specifically when W is associated to a finite root system…