BKP plane partitions

TL;DR

This paper derives a product formula for the generating function of volume-weighted plane partitions with specific path and coloring conditions using BKP neutral fermions, revealing new combinatorial structures.

Contribution

It introduces a novel application of BKP neutral fermions to obtain a product expression for a specialized class of plane partitions with path and coloring constraints.

Findings

Derived a product expression for the generating function.

Established a unique path connectivity condition.

Connected fermionic methods to combinatorial enumeration.

Abstract

Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.