- Title
- A combinatorial analysis of barred preferential arrangements
- Creator
- Nkonkobe, Sithembele
- ThesisAdvisor
- Murali, Venkat
- 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, pdf
- Publisher
- Rhodes University, Faculty of Science, Mathematics (Pure and Applied)
- Language
- English
- Rights
- Nkonkobe, Sithembele
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Collections
RU Department of Mathematics (Pure and Applied)
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