Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 1998. / A thesis submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in fulfilment of the requirements for the degree of
Doctor of Philosophy.
Johannesburg 1998 / Let A = (aij) be an m x n matrix. There is a natural way to associate a
poset PA with A. A jump in a linear extension of PA is a pair of consecutive
elements which are incomparable in Pa. The jump number of A is the minimum
number of jumps in any linear extension of PA. The maximum jump
number over a class of n x n matrices of zeros and ones with constant row and
column sum k, M (n, k), has been investigated in Chapter 2 and 3. Chapter
2 deals with extremization problems concerning M (n ,k). In Chapter 3, we
obtain the exact values for M (11,k). M(n,Q), M (n,n-3) and M(n,n-4).
The concept of frequency hyperrectangle generalizes the concept of latin
square. In Chapter 4 we derive a bound for the maximum number of mutually
orthogonal frequency hyperrectangles. Chapter 5 gives two algorithms to
construct mutually orthogonal frequency hyperrectangles.
Chapter 6 is devoted to some enumerative results about Carlitz compositions
(compositions with different adjacent parts).
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/14119 |
| Date | January 1999 |
| Creators | Cheng, Bo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (vi, 119 leaves), application/pdf |
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