A combinatorial analysis of higher order generalised geometric polynomials: A generalisation of barred preferential arrangements

https://doi.org/10.1016/j.disc.2019.111729Get rights and content
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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.

Keywords

Preferential arrangement
Barred preferential arrangement
Geometric polynomial

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