# A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements

## TL;DR

This paper generalizes barred preferential arrangements using generalized Stirling numbers, providing a unified combinatorial interpretation of geometric polynomials and exploring their asymptotic properties.

## Contribution

It introduces a new generalization of barred preferential arrangements based on generalized Stirling numbers, linking them to geometric polynomials.

## Key findings

- Unified combinatorial interpretation of geometric polynomials
- Asymptotic properties of generalized barred arrangements
- Extension of preferential arrangements using generalized Stirling numbers

## Abstract

A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers.