Complexity of sign imbalance, parity of linear extensions, and height 2 posets

TL;DR

This paper investigates the computational complexity of sign imbalance and parity of linear extensions in height 2 posets, providing new results and addressing a recent conjecture in the field.

Contribution

It establishes complexity results for sign imbalance and parity in height 2 posets and explores a conjecture by Chan and Pak.

Findings

Proves complexity results for sign imbalance in height 2 posets

Analyzes parity of linear extensions in specific poset classes

Addresses a recent conjecture by Chan and Pak

Abstract

Sign imbalance is a statistic on posets which counts the difference between the number of even and odd linear extensions. We prove complexity results about the sign imbalance and parity of linear extensions, focusing on the representative case of height 2 posets. We then consider a recent conjecture of Chan and Pak.