Proof of George Andrews's and David Robbins's q-TSPP Conjecture

TL;DR

This paper provides a proof for the long-standing conjecture that the orbit-counting generating function for totally symmetric plane partitions can be expressed as an explicit product formula, resolving a problem posed by Andrews and Robbins.

Contribution

The paper offers the first complete proof of the q-TSPP conjecture, confirming the explicit product formula for the generating function.

Findings

Confirmed the explicit product formula for the orbit-counting generating function

Resolved a conjecture independently posed by Andrews and Robbins in 1983

Established a new proof technique for symmetric plane partitions

Abstract

The conjecture that the orbit-counting generating function for totally symmetric plane partitions can be written as an explicit product formula, has been stated independently by George Andrews and David Robbins around 1983. We present a proof of this long-standing conjecture.