Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory
Author | : Shreejit Bandyopadhyay |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
ISBN-10 | : OCLC:1346413392 |
ISBN-13 | : |
Rating | : 4/5 (92 Downloads) |
Download or read book Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory written by Shreejit Bandyopadhyay and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation explores three related topics in the theory of integer partitions. We first revisit certain conjectures made by George Beck about the crank of a partition. We discuss a new approach to these conjectures by decomposing the relevant crank generating function and further explore connections with certain identities involving generalized Lambert series and Appell-Lerch sums. After that, we derive certain weighted generating functions of cranks by both analytic and combinatorial arguments. Lastly, we consider overpartition analogues for Bressoud's generalizations of the famous Rogers-Ramanujan identities. We discuss some new Rogers-Ramanujan type overpartition identities under certain constraints on odd and even parts of the partitions.