A note on a question due to A. Garsia

TL;DR

This paper discusses a permutation enumeration formula by Garsia, proving a stronger version under a specific conjecture, advancing understanding in algebraic combinatorics.

Contribution

It extends Garsia's permutation enumeration formula by establishing a stronger result contingent on a particular conjecture.

Findings

Proves a stronger version of Garsia's permutation enumeration formula.

Establishes the result under a specific conjecture.

Contributes to algebraic combinatorics and permutation enumeration theory.

Abstract

Adriano Garsia has provided an explicit formula to enumerate a certain class of permutations in the symmetric group S_n. In this short note, we prove a stronger version of the assertion under a specific conjecture.