Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593156 | Journal of Number Theory | 2016 | 24 Pages |
Abstract
This article is an extensive study of partitions with fixed number of odd and even-indexed odd parts. We use these partitions to generalize recent results of C. Savage and A. Sills. Moreover, we derive explicit formulas for generating functions for partitions with bounds on the largest part, the number of parts and with a fixed value of BG-rank or with a fixed value of alternating sum of parts. We extend the work of C. Boulet, and as a result, obtain a four-variable generalization of Gaussian binomial coefficients. In addition, we provide combinatorial interpretation of the Berkovich–Warnaar identity for Rogers–Szegő polynomials.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexander Berkovich, Ali Kemal Uncu,