This book describes and summarizes past work in important areas of combinatorics and computation, as well as gives directions for researchers working in these areas in the 21st century. It contains primarily survey papers and presents original research by Peter Fishburn, Jim Ho Kwak, Jaeun Lee, K.H. Kim, F.W. Roush and Susan Williams. The papers deal with some of the most exciting and promising developments in the areas of coding theory in relation to number theory, lattice theory and its applications, graph theory and its applications, topological techniques in combinatorics, symbolic dynamics and mathematical social science.
Author(s): J.H. Kwah, S. Hong, K.H. Kim, Sungpyo Hong, Jin Ho Kwak, Ki Hang Kim, Fred W. Roush
Edition: 1st
Publisher: World Scientific
Year: 2001
Language: English
Pages: 286
City: Singapore; River Edge, N.J
Foreword ......Page 6
CONTENTS ......Page 8
1 INTRODUCTION ......Page 9
2 POINT SETS FOR MONTE-CARLO METHODS ......Page 10
3 POINT SETS FOR QUASI-MONTE-CARLO METHODS ......Page 13
References ......Page 20
1 INTRODUCTION ......Page 21
2 ORDINAL PREFERENCES ......Page 24
3 COMPARABLE PREFERENCE DIFFERENCES ......Page 25
4 MULTIPLE ATTRIBUTES ......Page 26
5 TIME STREAMS ......Page 27
6 CHOICE FUNCTIONS ......Page 28
7 SOCIAL CHOICE FUNCTIONS ......Page 29
8 SUBSET RANKING AND CHOICE ......Page 31
9 LOTTERIES AND RISK ......Page 32
10 UNCERTAINTY ......Page 34
References ......Page 36
2 LIST OF APPLICABLE MATHEMATICS IN SOCIAL SCIENCE ......Page 38
3 SOCIAL WELFARE FUNCTIONS (SWF) ......Page 44
4 PROSPECTS ......Page 59
5 OPEN PROBLEMS ......Page 60
References ......Page 61
1 LINEAR DEPENDENCE WITHOUT SCALARS ......Page 64
2 BASIS EXCHANGE PROPERTIES ......Page 69
3 GEOMETRIC LATTICES ......Page 73
4 GRAPH THEORY WITHOUT VERTICES ......Page 78
5 GRAPH THEORY AND LEAN LINEAR ALGEBRA ......Page 80
6 VARIETIES OF FINITE MATROIDS ......Page 83
7 SECRET-SHARING MATROIDS ......Page 86
8 GREEDY ALGORITHMS, MATROID INTERSECTION, AND MATROID PARTITION......Page 88
9 MATRIX MULTIPLICATION AND THE CAUCHY-BINET IDENTITY ......Page 92
10 BASIS GENERATING FUNCTIONS AND THE MATRIX-TREE THEOREM ......Page 94
11 GENERIC RANK-GENERATING POLYNOMIALS ......Page 96
References ......Page 101
1 Definitions and Notations ......Page 105
2 Cycle permutation graphs and the double cosets of Dn in Sn ......Page 107
3 Graph coverings and subgroups of free groups ......Page 111
4 Regular coverings with abelian voltage groups and subgroups of free abelian groups ......Page 125
5 Regular coverings having dihedral voltage groups ......Page 134
6 Regular coverings; A general case ......Page 140
7 New classifications of branched coverings and the number of subgroups of a surface group ......Page 142
8 Distributions of branched surface coverings ......Page 157
References ......Page 167
1 Introduction ......Page 170
2 The Poset of Irreducibles ......Page 172
3 Applications ......Page 177
References ......Page 184
1 Introduction ......Page 186
2 Public-Key Cryptography ......Page 192
3 New Requirements ......Page 194
4 The Algorithmic Number Theory ......Page 196
5 Trapdoor One-Way Problems ......Page 201
6 Recapitulation ......Page 205
7 Application to Public Key Cryptography ......Page 206
8 Conclusion and Open Problems ......Page 211
References ......Page 212
2 Graph Coloring ......Page 218
3 The Second Concept: Intersection Graph ......Page 224
4 Third Concept: Competition Graph ......Page 233
References ......Page 239
1 INTRODUCTION ......Page 251
2 FUNDAMENTAL GROUP AND HOMOLOGY ......Page 252
3 REPRESENTATION OF CLOPEN SETS ......Page 259
4 ORBIT CLOSURE EQUIVALENCE ......Page 264
5 ACTION OF AUTOMORPHISMS ON ORDERED COHOMOLOGY ......Page 268
6 CONCLUSION ......Page 271
References ......Page 272
1 Introduction ......Page 274
2 Known Orientation ......Page 276
3 Unknown Orientation ......Page 278
4 Initial Values of Parameters and Independent Flipping ......Page 279
6 Conclusion ......Page 282
References ......Page 284
