An overpartition analogue of the $q$-binomial coefficients
Combinatorics
2014-12-30 v2 Number Theory
Abstract
We define an overpartition analogue of Gaussian polynomials (also known as -binomial coefficients) as a generating function for the number of overpartitions fitting inside the rectangle. We call these new polynomials over Gaussian polynomials or over -binomial coefficients. We investigate basic properties and applications of over -binomial coefficients. In particular, via the recurrences and combinatorial interpretations of over q-binomial coefficients, we prove a Rogers-Ramaujan type partition theorem.
Keywords
Cite
@article{arxiv.1410.5301,
title = {An overpartition analogue of the $q$-binomial coefficients},
author = {Jehanne Dousse and Byungchan Kim},
journal= {arXiv preprint arXiv:1410.5301},
year = {2014}
}
Comments
v2: new section added about another way of proving our theorems using q-series identities