Enumeration of $n$-plexes

TL;DR

This paper corrects and clarifies the formulas for enumerating n-plexes, addressing previous typographical errors in key mathematical expressions related to cycle indices and counts.

Contribution

It provides the accurate formulas for enumerating n-plexes, correcting prior typographical errors in the cycle index and enumeration formulas.

Findings

Corrected formula for cycle index Z(S_p^{(r)})

Accurate calculation of s_p^n, the number of n-plexes

Enhanced understanding of n-plex enumeration methods

Abstract

Palmer provides a method of enumerating $n$-plexes, however it has some typographical errors in the formula for the cycle index $Z(S_p^{(r)})$ and the values of $s_p^n$, the number of $n$-plexes on $p$ points. This article is intended to provide the correct formulas.