Descripción del título
Combinatorics of finite set...
Monografía
monografia Rebiun05647011 https://catalogo.rebiun.org/rebiun/record/Rebiun05647011 020125r20021987nyu 001 0 eng 0486422577 pbk.) CBUC 991029276929706706 UPM 991003674809704212 UVA. spa Anderson, Ian Combinatorics of finite sets Ian Anderson Mineola, N.Y. Dover Publications 2002 Mineola, N.Y. Mineola, N.Y. Dover Publications xv, 250 p. 22 cm xv, 250 p. Dover books on mathematics " ... 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 Bibliografía p. 241-248. Indices Machine generated contents note: 1. Introduction and Sperner's theorem -- 1.1 A simple intersection result -- 1.2 Sperner's theorem -- 1.3 A theorem of Bollobas -- Exercises 1 -- 2. Normalized matchings and rank numbers -- 2.1 Sperner's proof -- 2.2 Systems of distinct representatives -- 2.3 LYM inequalities and the normalized matching -- property -- 2.4 Rank numbers: some examples -- Exercises 2 -- 3. Symmetric chains -- 3.1 Symmetric chain decompositions -- 3.2 Dilworth's theorem -- 3.3 Symmetric chains for sets -- 3.4 Applications -- 3.5 Nested chains -- 3.6 Posets with symmetric chain decompositions -- Exercises 3 -- 4. Rank numbers for multisets -- 4.1 Unimodality and log concavity -- 4.2 The normalized matching property -- 4.3 The largest size of a rank number -- Exercises 4 -- 5. Intersecting systems and the Erdos-Ko-Rado -- theorem -- 5.1 The EKR theorem -- 5.2 Generalizations of EKR -- 5.3 Intersecting aintichains with large members -- 5.4 A probability application of EKR -- 5.5 Theorems of Milner and Katona -- 5.6 Some results related to the EKR theorem -- Exercises 5 -- 6. Ideals and a lemma of Kleitman -- 6.1 Kleitman's lemma -- 6.2 The Ahlswede-Daykin inequality -- 6.3 Applications of the FKG inequality to probability -- theory -- 6.4 Chvatal's conjecture -- Exercises 6 -- 7. The Kruskal-Katona theorem -- 7.1 Order relations on subsets -- 7.2 The i-binomial representation of a number -- 7.3 The Kruskal-Katona theorem -- 7.4 Some easy consequences of Kruskal-Katona -- 7.5 Compression -- Exercises 7 -- 8. Antichains -- 8.1 Squashed antichains -- 8.2 Using squashed antichains -- 8.3 Parameters of intersecting antichains -- Exercises 8 -- 9. The generalized Macaulay theorem for multisets -- 9.1 The theorem of Clements and Lindstrom -- 9.2 Some corollaries -- 9.3 A minimization problem in coding theory -- 9.4 Uniqueness of maximum-sized antichains in -- multisets -- Exercises 9 -- 10. Theorems for multisets -- 10.1 Intersecting families -- 10.2 Antichains in multisets -- 10.3 Intersecting antichains -- Exercises 10 -- 11. The Littlewood-Offord problem -- 11.1 Early results -- 11.2 M-part Sperner theorems -- 11.3 Littlewood-Offord results -- Exercises 11 -- 12. Miscellaneous methods -- 12.1 The duality theorem of linear programming -- 12.2 Graph-theoretic methods -- 12.3 Using network flow -- Exercises 12 -- 13. Lattices of antichains and saturated chain partitions -- 13.1 Antichains -- 13.2 Maximum-sized antichains -- 13.3 Saturated chain partitions -- 13.4 The lattice of k-unions -- Exercises 13 -- Hints and solutions -- References -- Index Conjuntos, Teoría de Análisis combinatorio Dover books on mathematics