Stirling permutations, cycle structures of permutations and perfect matchings

TL;DR

This paper introduces a unified combinatorial framework linking Stirling permutations, permutation cycle structures, and perfect matchings using MY-sequences, revealing new interpretations of Eulerian polynomials.

Contribution

It provides a novel combinatorial approach connecting these concepts and offers a new interpretation of Eulerian polynomials through MY-sequences.

Findings

Eulerian polynomials have a simple combinatorial interpretation via MY-sequences

Established connections between Stirling permutations, cycle structures, and perfect matchings

Developed a unified combinatorial framework for these concepts

Abstract

In this paper we provide a unified combinatorial approach to establish a connection between Stirling permutations, cycle structures of permutations and perfect matchings. The main tool of our investigations is MY-sequences. In particular, we discover that the Eulerian polynomials have a simple combinatorial interpretation in terms of some statistics on MY-sequences.