A combinatorial analysis of barred preferential arrangements
- Authors: Nkonkobe, Sithembele
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/36228 , 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.
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- Date Issued: 2016
An investigation of participative management in a museum in the Eastern Cape, South Africa
- Authors: Madinda, Nozipho
- Date: 2016
- Subjects: Museums -- South Africa -- Eastern Cape -- Management , Management -- Employee participation , Albany Museum (Grahamstown, South Africa)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2068 , http://hdl.handle.net/10962/d1020847
- Description: The purpose of my research was to investigate participative management at the Albany Museum with a view to generating knowledge and insights that can be used to support senior management’s engagement with participative management at mid-management level. My interest was to investigate participative management with regards to five HODs of the Albany Museum with a view to generating knowledge and insights that can be used to support senior management’s engagement with participative management at mid-management level. The research was informed by the interpretive paradigm. The interpretive paradigm does not concern itself with the search for broadly applicable laws and rules but rather seeks to produce descriptive analyses that emphasise deep interpretation and understanding of social phenomena through the meaning that the people assign to them. This study is mostly descriptive and presents the reality of participants from their own experience. Semi-structured interviews and observation capture ‘insider’ knowledge that is part of an interpretive methodology. The study found that participative management was both understood and generally accepted as a good way to manage an organisation, and even members who were critical of it could see its benefits. However, the fractured and diversified structure of the organisation calls for a particularly skillful application of this management approach, one which would also demand leadership and a greater sense of working towards what are called collegial models of management. Whether this is in fact desirable for a museum is debatable.
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- Date Issued: 2016