A combinatorial analysis of barred preferential arrangements

Title: A combinatorial analysis of barred preferential arrangements
Creator: Nkonkobe, Sithembele
Date Issued: 2016
Date: 2016
Type: Thesis
Type: Doctoral
Type: PhD
Identifier: http://hdl.handle.net/10962/36228
Identifier: vital:24530
Description: For a non-negative integer n an ordered partition of a set Xn with n distinct elements is called a preferential arrangement (PA). A barred preferential arrangement (BPA) is a preferential arrangement with bars in between the blocks of the partition. An integer sequence an associated with the counting PA's of Xn has been intensely studied over a century and a half in many different contexts. In this thesis we develop a unified combinatorial framework to study the enumeration of BPAs and a special subclass of BPAs. The results of the study lead to a positive settlement of an open problem and a conjecture by Nelsen. We derive few important identities pertaining to the number of BPAs and restricted BPAs of an n element set using generating- functionology. Later we show that the number of restricted BPAs of Xn are intricately related to well-known numbers such as Eulerian numbers, Bell numbers, Poly-Bernoulli numbers and the number of equivalence classes of fuzzy subsets of Xn under some equivalent relation.
Format: 89 leaves
Format: pdf
Publisher: Rhodes University
Publisher: Faculty of Science, Mathematics (Pure and Applied)
Language: English
Rights: Nkonkobe, Sithembele

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