Combinatorics of finite sets
By: Ian Anderson.
Series: Dover books on mathematics
Publisher: Dover Publications
Published: 2002
Place of publication: Mineola, N.Y
Language: eng
Number of pages: 250
Subjects: Set theory.; Combinatorial analysis.
Notes: Includes bibliographical references (p. 241-248) and index.
" ... a corrected republication of the work as published by Oxford University Press, Oxford, England, and New York, in 1989 (first publication: 1987)"--T.p. verso.
Table of contents: title: Machine generated contents note: 1. Introduction and Sperner's theorem; title: 1.1 A simple intersection result; title: 1.2 Sperner's theorem; title: 1.3 A theorem of Bollobas; title: Exercises 1; title: 2. Normalized matchings and rank numbers; title: 2.1 Sperner's proof; title: 2.2 Systems of distinct representatives; title: 2.3 LYM inequalities and the normalized matching; title: property; title: 2.4 Rank numbers: some examples; title: Exercises 2; title: 3. Symmetric chains; title: 3.1 Symmetric chain decompositions; title: 3.2 Dilworth's theorem; title: 3.3 Symmetric chains for sets; title: 3.4 Applications; title: 3.5 Nested chains; title: 3.6 Posets with symmetric chain decompositions; title: Exercises 3; title: 4. Rank numbers for multisets; title: 4.1 Unimodality and log concavity; title: 4.2 The normalized matching property; title: 4.3 The largest size of a rank number; title: Exercises 4; title: 5. Intersecting systems and the Erdos-Ko-Rado; title: theorem; title: 5.1 The EKR theorem; title: 5.2 Generalizations of EKR; title: 5.3 Intersecting aintichains with large members; title: 5.4 A probability application of EKR; title: 5.5 Theorems of Milner and Katona; title: 5.6 Some results related to the EKR theorem; title: Exercises 5; title: 6. Ideals and a lemma of Kleitman; title: 6.1 Kleitman's lemma; title: 6.2 The Ahlswede-Daykin inequality; title: 6.3 Applications of the FKG inequality to probability; title: theory; title: 6.4 Chvatal's conjecture; title: Exercises 6; title: 7. The Kruskal-Katona theorem; title: 7.1 Order relations on subsets; title: 7.2 The i-binomial representation of a number; title: 7.3 The Kruskal-Katona theorem; title: 7.4 Some easy consequences of Kruskal-Katona; title: 7.5 Compression; title: Exercises 7; title: 8. Antichains; title: 8.1 Squashed antichains; title: 8.2 Using squashed antichains; title: 8.3 Parameters of intersecting antichains; title: Exercises 8; title: 9. The generalized Macaulay theorem for multisets; title: 9.1 The theorem of Clements and Lindstrom; title: 9.2 Some corollaries; title: 9.3 A minimization problem in coding theory; title: 9.4 Uniqueness of maximum-sized antichains in; title: multisets; title: Exercises 9; title: 10. Theorems for multisets; title: 10.1 Intersecting families; title: 10.2 Antichains in multisets; title: 10.3 Intersecting antichains; title: Exercises 10; title: 11. The Littlewood-Offord problem; title: 11.1 Early results; title: 11.2 M-part Sperner theorems; title: 11.3 Littlewood-Offord results; title: Exercises 11; title: 12. Miscellaneous methods; title: 12.1 The duality theorem of linear programming; title: 12.2 Graph-theoretic methods; title: 12.3 Using network flow; title: Exercises 12; title: 13. Lattices of antichains and saturated chain partitions; title: 13.1 Antichains; title: 13.2 Maximum-sized antichains; title: 13.3 Saturated chain partitions; title: 13.4 The lattice of k-unions; title: Exercises 13; title: Hints and solutions; title: References; title: Index.