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Asymptotics of partition parts in arithmetic progressions
Kathrin Bringmann, Caner Nazaroglu, Jan-Willem M. van Ittersum
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying t…
Overpartitions with parts separated by parity
Kathrin Bringmann, Catherine Cossaboom, William Craig
In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose part…
Ramanujan's partition generating functions modulo
Kathrin Bringmann, William Craig, Ken Ono
For the partition function , Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\in…
Eisenstein-type series associated to partition ranks
Kathrin Bringmann, Badri Vishal Pandey, Jan-Willem van Ittersum
In this paper, we introduce a class of functions that behave like classical Eisenstein series in many ways, but with a key distinction: only their non-holomorphic completions trans…
Statistics for random representations of Lie algebras
Walter Bridges, Kathrin Bringmann, Caner Nazaroglu
In this paper we investigate how a typical, large-dimensional representation looks for a complex Lie algebra. In particular, we study the family o…