Poly-Cauchy numbers -- the combinatorics behind

TL;DR

This paper introduces poly-Cauchy permutations and demonstrates their properties through combinatorial proofs, highlighting the elegance of elementary combinatorial methods in understanding poly-Cauchy numbers.

Contribution

It defines poly-Cauchy permutations and provides combinatorial proofs for identities involving poly-Cauchy numbers and their generalizations.

Findings

Poly-Cauchy permutations are enumerated by poly-Cauchy numbers.

Several identities involving poly-Cauchy numbers are proven combinatorially.

The approach showcases the power of elementary combinatorial techniques.

Abstract

We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some of their generalizations. The aim of this work is to demonstrate the power and beauty of the elementary combinatorial approach.