4 papers
Alder-type partition inequality at the general level
Haein Cho, Soon-Yi Kang, Byungchan Kim
A Known Alder-type partition inequality of level , which involves the second Rogers-Ramanujan identity when the level is 2, states that the number of partitions of into…
On the asymptotic behavior of unimodal rank generating functions
Kathrin Bringmann, Byungchan Kim
In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these con…
An overpartition analogue of the -binomial coefficients
Jehanne Dousse, Byungchan Kim
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 $…
Dissections of a "strange" function
Scott Ahlgren, Byungchan Kim
The "strange" function of Kontsevich and Zagier is defined by \[F(q):=\sum_{n=0}^\infty(1-q)(1-q^2)\dots(1-q^n).\] This series is defined only when is a root of unity, and prov…