Jump numbers, hyperrectangles and Carlitz compositions
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 mat...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | en |
| Published: |
2014
|
| Subjects: | |
| Online Access: | Cheng, Bo (1999) Jump numbers, hyperrectangles and Carlitz compositions, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/14119> http://hdl.handle.net10539/14119 |
| Summary: | 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). |
|---|