Compositions that are palindromic modulo $m$

TL;DR

This paper generalizes the concept of parity palindromic compositions to compositions palindromic modulo m, providing new combinatorial proofs for specific cases and extending previous results.

Contribution

It introduces a broader class of palindromic compositions modulo m and offers combinatorial proofs for cases m=2 and m=3, advancing understanding in this area.

Findings

Extended parity palindromic compositions to modulo m

Provided combinatorial proofs for m=2 and m=3 cases

Connected new results to previous parity composition work

Abstract

In recent work, G. E. Andrews and G. Simay prove a surprising relation involving parity palindromic compositions, and ask whether a combinatorial proof can be found. We extend their results to a more general class of compositions that are palindromic modulo $m$, that includes the parity palindromic case when $m=2$. We then provide combinatorial proofs for the cases $m=2$ and $m=3$.