4 citations · 13 across the 35 of their papers we have counts for
39 papers
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 int…
Franklin's identity for -color partitions and companion Beck-type identities
Cristina Ballantine, Roberto Tauraso
We show that some classical identities valid for ordinary partitions have precise analogues for -color partitions, that is partitions in which a part of size can occur…
Reciprocals of Subsum Polynomials
Cristina Ballantine, George Beck, Brooke Feigon +1
We introduce the subsum polynomial of a partition defined by . We study the sum of reciprocals of $\mathrm{s…
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…
Lambert series and double Lambert series
Tewodros Amdeberhan, George E. Andrews, Cristina Ballantine
We consider relationships between classical Lambert series, multiple Lambert series and classical -series of the Rogers-Ramanujan type. We conclude with a contemplation on the A…
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…