Enumerative considerations of SDR's and latin rectangles

Abstract

The art of counting is interesting but often 120000103 a difficult task. It requires computational skills^ ' .. ability to recognise similar patterns and a little mastery of general principles and simplification techniques. This thesis deals with the enumsrative aspects of systems of Distinct xtopresentatives (SDR's) and Latin rectangles. It is divided into four chapters and is based on the author's papers [2], [16], [I7]s [18], [1 9 l» The first chapter gives a general introduction, definitions and notations used in the thesis, a brief survey of earlier results and a summary of the results of the thesis. The second chapter deals with the enumeration of SDit's and symbolic representations. The third chapter, which contains the main theorems, deals v/ith the enumeration of Latin rectangles, and chromatic polynomials of line graphs of complete bipartite graphs. Two-line, three-line and fourline Latin rectangles are enumerated. The fourth chapter contains proofs of several recurrence relations for two-line, three-line generalis.ed and ordinary Latin rectangles and for very reduced 4 by n Latin rectangles. Though the chapters are numbered by lioman numerals, equations, theorems etc. are numbered in double-point style. Thus equation (3 .1 .5 ) or merely (3 .1 .5) means equation 5 of section 1 in Chapter III. A lift of symbols is given at the end