Equidistributed statistics on Fishburn matrices and permutations

TL;DR

This paper constructs a bijection between restricted permutations and Fishburn matrices, demonstrating the equidistribution of specific statistics, thus confirming Jelínek's conjecture.

Contribution

It provides the first explicit bijection that proves the equidistribution of statistics between permutations and Fishburn matrices, confirming a longstanding conjecture.

Findings

Established a bijection verifying equidistribution of statistics

Confirmed Jelínek's conjecture on Fishburn matrices and permutations

Enhanced understanding of combinatorial structures and their relationships

Abstract

Recently, Jel\'inek conjectured that there exists a bijection between certain restricted permutations and Fishburn matrices such that the bijection verifies the equidistribution of several statistics. The main objective of this paper is to establish such a bijection.