11 citations · 25 across the 12 of their papers we have counts for
12 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…
Asymptotics and sign patterns for coefficients in expansions of Habiro elements
Ankush Goswami, Abhash Kumar Jha, Byungchan Kim +1
We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics…
Dissections of strange -series
Scott Ahlgren, Byungchan Kim, Jeremy Lovejoy
In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontse…
Congruences for a mock modular form on and the smallest parts function
Scott Ahlgren, Byungchan Kim
Using a family of mock modular forms constructed by Zagier, we study the coefficients of a mock modular form of weight on modulo primes $\el…
On spt-crank type functions
Min-Joo Jang, Byungchan Kim
In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function , which is closely related to Ramanujan's third order mock theta function $ω(…
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…
On the number of even and odd strings along the over partitions of n
Byungchan Kim, Eunmi Kim, Jeehyeon Seo
Recently, Andrews, Chan, Kim and Osburn introduced the even strings and the odd strings in the overpartitions. We show that their conjecture holds for large…
The first positive rank and crank moments for overpartitions
George Andrews, Song Heng Chan, Byungchan Kim +1
In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also h…
Mock theta functions and weakly holomorphic modular forms modulo 2 and 3
Scott Ahlgren, Byungchan Kim
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly ho…
Eichler integrals and harmonic weak Maass forms
Dohoon Choi, Byungchan Kim, Subong Lim
Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular…