Committees for Pattern Recognition: Infeasible Systems of Linear Inequalities, Hyperplane Arrangements, and Realizable Oriented Matroids

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents IX
4. Committees for Pattern Recognition: Infeasible Systems of Linear Inequalities, Hyperplane Arrangements, and Realizable Oriented Matroids 1
5. 1. Oriented Matroids, the Pattern Recognition Problem, and Tope Committees 5
6. 2. Boolean Intervals 54
7. 3. Dehn–Sommerville Type Relations 67
8. 4. Farey Subsequences 82
9. 5. Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets 88
10. 6. Committees of Set Families, and Relative Blocking Constructions in Posets 118
11. 7. Layers of Tope Committees 143
12. 8. Three-Tope Committees 150
13. 9. Halfspaces, Convex Sets, and Tope Committees 157
14. 10. Tope Committees and Reorientations of Oriented Matroids 167
15. 11. Topes and Critical Committees 174
16. 12. Critical Committees and Distance Signals 181
17. 13. Symmetric Cycles in the Hypercube Graphs 188
18. Bibliography 199
19. List of Notation 209
20. Index 217