Combinatorial & computational mathematics: present and future: Pohang, the Republic of Korea, 15-17 February 2000

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