From the 1 of 6 linked papers with an AI index.
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Identities involving the number of missing integers in partitions - combinatorial proofs
Joselyne Aniceto, Cristina Ballantine
A missing integer in a partition is a positive integer less than the largest part of that does not appear as a part in . In the recent paper On the number of missing…
Franklin's identity for -color partitions and companion Beck-type identities
Cristina Ballantine, Roberto Tauraso
The paper extends classic partition identities, including Franklin's theorem and Beck-type identities, to partitions where each part can appear in multiple colors, providing both a…
On partitions associated with elementary symmetric polynomials
Cristina Ballantine, Shaheen Nazir, Bridget Eileen Tenner +2
The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the el…
Elementary symmetric partitions
Cristina Ballantine, George Beck, Mircea Merca +1
Let e_k(x_1,...,x_l) be an elementary symmetric polynomial and let mu = (mu_1,...,mu_l) be an integer partition. Define pre_k(mu) to be the partition whose parts are the summands i…
Partitions and elementary symmetric polynomials -- an experimental approach
Cristina Ballantine, George Beck, Mircea Merca
Given a partition , we write for the elementary symmetric polynomial evaluated at the parts of and for the sum of a…
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…