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We write down an explicit conjecture for the instanton partition functions in 4d N = 2 SU(N) gauge theories in the presence of a certain type of surface operator.
We study the rate of growth of p(n, S,M), the number of partitions of n whose parts all belong to S and whose multiplicities all belong to M, where S (resp. M) are given infinite sets of positive (res...
We introduce the growth partition function Z􀀀,G(t)associated with any cancellative infinite monoid 􀀀 with a finite generator system G. It is a power series in t whose coefficients l...
Here we prove that Benford’s law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessa...
The partition function for a canonical ensemble of 2D Coulomb charges in a background potential (the Dyson gas) is realized as a vacuum expectation value of a group-like element constructed in terms o...
We propose to use the identiˉcation of topological string partition functions as equivariant indices on framed moduli spaces of instantons to study the Gopakumar-Vafa conjecture for some local Calabi-...
We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graph...
We present exact calculations of the partition function $Z$ of the $q$-state Potts model and its generalization to real $q$, the random cluster model, for arbitrary temperature on $n$-vertex ladder gr...

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