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

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.Mathematics Subject Classifications : 05A15, 05A16, 05A18, 05A19, 11B73, 11B83 Keyword(s):preferential arrangement, barred preferential arrangement, geometric polynomial.