Topics in combinatorial mathematics

These notes were produced at the 1972 Cooperative Summer Seminar conducted at Williams College by the Mathematical Associa- tion of America. This Seminar was financed by the National Science Foundation. TOPICS IN COMBINATORIAL MATHEMATICS 1 ......Page 1 FORWARD 2......Page 2 TABLE OF CONTENTS 4......Page 4 PREFACE 5 ......Page 5 I. RAMSEY'S THEOREM 7 ......Page 7 II. SPERNER1S THEOREM AND RELATED TOPICS 25......Page 25 III. DILWORTH1S THEOREM AND MATCHING THEORY 43 ......Page 43 IV. PLANE PARTITIONS AND YOUNG TABLEAUX 72......Page 72 V. TOPICS IN THE THEORY OF GRAPHS I - PATH PROBLEMS 93 ......Page 93 VI. TOPICS IN THE THEORY OF GRAPHS II - COLORABILITY 110 ......Page 110 VII. A COMBINATIONAL STUDY OF SCHEDULING ALGORITHMS 153 ......Page 153 VIII. ANALYSIS OF SORTING ALGORITHMS 169 ......Page 169 IX. POLYA יS THEORY OF COUNTING 189......Page 189 X. INVERSION FORMULAE 202......Page 202 XI. ORTHOGONAL LATIN SQUARES 220 ......Page 220 XII. A THEORY OF BINOMIAL ENUMERATION 244 ......Page 244