Gupta, Ramanujan, Dyson and Ehrhart: Formulas for Partition Functions, Congruences, Cranks, and Polyhedral Geometry

Abstract

We will revisit Gupta's result regarding properties of a formula for restricted partitions and generalize this. We will then use this result to prove an infinite family of congruences for a certain restricted partition function. We find and prove combinatorial witnesses, also known as cranks, for the congruences using polyhedral geometry.