Congruences modulo powers of $2$ for the number of unique path partitions

TL;DR

This paper determines the congruence class modulo 16 of the number of unique path partitions of n, extending previous work and providing new insights into their arithmetic properties.

Contribution

It generalizes earlier results by computing the exact congruence class modulo 16 for unique path partitions, advancing understanding of their number-theoretic behavior.

Findings

Computed the congruence class modulo 16 for unique path partitions

Extended previous results to a broader class of partitions

Provided new formulas or methods for analyzing partition congruences

Abstract

We compute the congruence class modulo 16 of the number of unique path partitions of $n$ (as defined by Olsson), thus generalising previous results by Bessenrodt, Olsson and Sellers [Ann. Combin. 13 (2013), 591-602].