Generalized permutations related to the degenerate Eulerian numbers

TL;DR

This paper introduces a new combinatorial model that generalizes permutations and degenerate Eulerian numbers, offering new insights and proofs for their properties.

Contribution

It presents a novel combinatorial framework that extends the classical permutation concept and degenerate Eulerian numbers, filling gaps in their combinatorial understanding.

Findings

Provides a generalized combinatorial model for permutations

Derives new combinatorial proofs for degenerate Eulerian numbers

Extends the theory of degenerate Eulerian polynomials and numbers

Abstract

In this work we propose a combinatorial model that generalizes the standard definition of permutation. Our model generalizes the degenerate Eulerian polynomials and numbers of Carlitz from 1979 and provides missing combinatorial proofs for some relations on the degenerate Eulerian numbers.