arXiv subjects

Sithembele Nkonkobe

Publications and source records attributed to Sithembele Nkonkobe.

6 recordsLinked to original sources

arXiv2026

Combinatorics of higher order degenerate $r$-DERANGED Bell Numbers

When one inserts a number of identical bars in between blocks of an ordered set partition, they obtain a barred preferential arrangement. In this study we define a new generalization of barred preferential arrangements, by considering barred preferential arrangements with no fixed blocks, and where $r$ fixed elements on each section of the barred preferential arrangement are singletons. We derive several combinatorial identities for the number of these barred preferential arrangements. We also provide some asymptotic results.

math.GM↗

arXiv2026

Partial degenerate Stirling numbers

In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.

math.CO↗

arXiv2025

The Telephone Exchange Problem Revisited: A Combinatorial Approach

In this study we revisit the telephone exchange problem. We discuss a generalization of the telephone exchange problem by discuss two generalizations of the Bessel polynomials. We study combinatorial properties of these polynomials, and show how the numbers are related to the well known Whitney numbers and Dowling numbers

math.CO↗

arXiv2024

Extended Equivalence of Fuzzy Sets

Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and derive some important combinatorial formulae for the number of such tight fuzzy subsets of an n-element set where n is a natural number. We also offer some asymptotic results

math.GM↗

arXiv2019

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

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.

math.CO↗

arXiv2019

Generalised Barred Preferential Arrangements

A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred preferential arrangements whose elements are colored with a number of available colors.

math.CO↗