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

2019/08/14 by Sithembele Nkonkobe, Nkonkobe, Sithembele, Beáta Bényi +5 · 4 citations
Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1908.05014

openalex publication_date 2019/08/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

A barred preferential arrangement is a preferential arrangement, onto which\nin-between the blocks of the preferential arrangement a number of identical\nbars are inserted. We offer a generalisation of barred preferential\narrangements by making use of the generalised Stirling numbers proposed by Hsu\nand Shiue (1998). We discuss how these generalised barred preferential\narrangements offer a unified combinatorial interpretation of geometric\npolynomials. We also discuss asymptotic properties of these numbers.\n

Cited by

• Combinatorics of higher order degenerate r-DERANGED Bell Numbers
• Higher Order r-Dowling polynomials
• Partial Deranged Bell Numbers and Their Combinatorial Properties
• The Telephone Exchange Problem Revisited: A Combinatorial Approach

Related

• A Second Type Of Higher Order Generalised Geometric Polynomials and\n Higher Order Generalised Euler Polynomials
• Higher Order r-Dowling polynomials
• Generalised Barred Preferential Arrangements
• Barred Preferential Arrangements
• Combinatorics of higher order degenerate r-DERANGED Bell Numbers