The 2-adic valuation of plane partitions and totally symmetric partitions

TL;DR

This paper proves a conjecture relating the 2-adic valuation of plane partitions and totally symmetric plane partitions within an n-cube, showing a parity-dependent inequality.

Contribution

It confirms a conjecture about the 2-adic valuations of plane partitions and symmetric plane partitions, establishing a parity-based inequality.

Findings

For even n, the 2-adic valuation of plane partitions exceeds that of symmetric ones.

For odd n, the 2-adic valuation of plane partitions is less than that of symmetric ones.

The conjecture of Amdeberhan and Moll is validated.

Abstract

This paper confirms a conjecture of Amdeberhan and Moll that the power of 2 dividing the number of plane partitions in an n-cube is greater than the power of 2 dividing the number of totally symmetric plane partitions in the same cube when n is even, and less when n is odd.