From the 1 of 5 linked papers with an AI index.
5 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…
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…
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 $\ma…
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…