Charge functions for all dimensional partitions

TL;DR

This paper explores charge functions for n-dimensional partitions, providing explicit formulas for odd dimensions, conjecturing and proving formulas for even dimensions, with verification up to 8D.

Contribution

It introduces a conjecture for charge functions in all even dimensions and proves it for 6D, expanding understanding of n-dimensional partition charge functions.

Findings

Conjectured charge function formula for all even dimensions.

Proved the formula rigorously for 6D.

Numerically verified the formula for 8D.

Abstract

The charge functions for n-dimensional partitions are known for n=2,3,4 in the literature. We give the expression for arbitrary odd dimension in a recent work, and now further conjecture a formula for all even dimensional cases. This conjecture is proved rigorously for 6D, and numerically verified for 8D.