An equivalence of multistatistics on permutations

TL;DR

This paper proves a conjecture about the equivalence of two sets of permutation statistics by constructing a bijection using Catalan-related objects, also introducing a new class-preserving bijection.

Contribution

It establishes the equivalence of two permutation statistic triples and introduces a novel co-sylvester class-preserving bijection.

Findings

Proves a conjecture on permutation statistics equivalence.

Constructs a bijection via Catalan objects related to PASEP.

Provides a new class-preserving bijection on permutations.

Abstract

We prove a conjecture of J.-C. Novelli, J.-Y. Thibon, and L. K. Williams (2010) about an equivalence of two triples of statistics on permutations. To prove this conjecture, we construct a bijection through different combinatorial objects, starting with a Catalan based object related to the PASEP. As a byproduct of this research, we also provide a new co-sylvester class-preserving bijection on permutations.