{"product_id":"combinatorics-of-finite-sets","title":"Combinatorics of Finite Sets","description":"\n\u003ctable align=\"center\" border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"100%\"\u003e\n\u003ctr\u003e\n\u003ctd class=\"productDetailSmallElements\"\u003e\n\u003cp\u003e\n\u003cstrong\u003eMarc Notes\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tMachine 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; ... 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;Includes bibliographical references (p. 241-248) and index.\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003eTable of Contents\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tNotation \n\u003cbr\u003e1. Introduction and Sperner's theorem \n\u003cbr\u003e 1.1 A simple intersection result \n\u003cbr\u003e 1.2 Sperner's theorem \n\u003cbr\u003e 1.3 A theorem of Bollobás \n\u003cbr\u003e Exercises 1 \n\u003cbr\u003e2. Normalized matchings and rank numbers \n\u003cbr\u003e 2.1 Sperner's proof \n\u003cbr\u003e 2.2 Systems of distinct representatives \n\u003cbr\u003e 2.3 LYM inequalities and the normalized matching property \n\u003cbr\u003e 2.4 Rank numbers: some examples \n\u003cbr\u003e Exercises 2 \n\u003cbr\u003e3. Symmetric chains \n\u003cbr\u003e 3.1 Symmetric chain decompositions \n\u003cbr\u003e 3.2 Dilworth's theorem \n\u003cbr\u003e 3.3 Symmetric chains for sets \n\u003cbr\u003e 3.4 Applications \n\u003cbr\u003e 3.5 Nested Chains \n\u003cbr\u003e 3.6 Posets with symmetric chain decompositions \n\u003cbr\u003e Exercises 3 \n\u003cbr\u003e4. Rank numbers for multisets \n\u003cbr\u003e 4.1 Unimodality and log concavity \n\u003cbr\u003e 4.2 The normalized matching property \n\u003cbr\u003e 4.3 The largest size of a rank number \n\u003cbr\u003e Exercises 4 \n\u003cbr\u003e5. Intersecting systems and the Erdös-Ko-Rado theorem \n\u003cbr\u003e 5.1 The EKR theorem \n\u003cbr\u003e 5.2 Generalizations of EKR \n\u003cbr\u003e 5.3 Intersecting antichains with large members \n\u003cbr\u003e 5.4 A probability application of EKR \n\u003cbr\u003e 5.5 Theorems of Milner and Katona \n\u003cbr\u003e 5.6 Some results related to the EKR theorem \n\u003cbr\u003e Exercises 5 \n\u003cbr\u003e6. Ideals and a lemma of Kleitman \n\u003cbr\u003e 6.1 Kleitman's lemma \n\u003cbr\u003e 6.2 The Ahlswede-Daykin inequality \n\u003cbr\u003e 6.3 Applications of the FKG inequality to probability theory \n\u003cbr\u003e 6.4 Chvátal's conjecture \n\u003cbr\u003e Exercises 6 \n\u003cbr\u003e7. The Kruskal-Katona theorem \n\u003cbr\u003e 7.1 Order relations on subsets \n\u003cbr\u003e 7.2 The l-binomial representation of a number \n\u003cbr\u003e 7.3 The Kruskal-Katona theorem \n\u003cbr\u003e 7.4 Some easy consequences of Kruskal-Katona \n\u003cbr\u003e 7.5 Compression \n\u003cbr\u003e Exercises 7 \n\u003cbr\u003e8. Antichains \n\u003cbr\u003e 8.1 Squashed antichains \n\u003cbr\u003e 8.2 Using squashed antichains \n\u003cbr\u003e 8.3 Parameters of intersecting antichains \n\u003cbr\u003e Exercises 8 \n\u003cbr\u003e9. The generalized Macaulay theorem for multisets \n\u003cbr\u003e 9.1 The theorem of Clements and Lindström \n\u003cbr\u003e 9.2 Some corollaries \n\u003cbr\u003e 9.3 A minimization problem in coding theory \n\u003cbr\u003e 9.4 Uniqueness of a maximum-sized antichains in multisets \n\u003cbr\u003e Exercises 9 \n\u003cbr\u003e10. Theorems for multisets \n\u003cbr\u003e 10.1 Intersecting families \n\u003cbr\u003e 10.2 Antichains in multisets \n\u003cbr\u003e 10.3 Intersecting antichains \n\u003cbr\u003e Exercises 10 \n\u003cbr\u003e11. The Littlewood-Offord problem \n\u003cbr\u003e 11.1 Early results \n\u003cbr\u003e 11.2 M-part Sperner theorems \n\u003cbr\u003e 11.3 Littlewood-Offord results \n\u003cbr\u003e Exercises 11 \n\u003cbr\u003e12. Miscellaneous methods \n\u003cbr\u003e 12.1 The duality theorem of linear programming \n\u003cbr\u003e 12.2 Graph-theoretic methods \n\u003cbr\u003e 12.3 Using network flow \n\u003cbr\u003e Exercises 12 \n\u003cbr\u003e13. Lattices of antichains and saturated chain partitions \n\u003cbr\u003e 13.1 Antichains \n\u003cbr\u003e 13.2 Maximum-sized antichains \n\u003cbr\u003e 13.3 Saturated chain partitions \n\u003cbr\u003e 13.4 The lattice of k-unions \n\u003cbr\u003e Exercises 13 \n\u003cbr\u003e Hints and solutions; References; Index\u003cbr\u003e\u003cbr\u003e\n\u003cstrong\u003ePublisher Marketing\u003c\/strong\u003e:\u003cbr\u003e\n\t\t\t\t\t\t\t\tAmong other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.\u003cbr\u003e\u003cbr\u003e\n\u003c\/p\u003e\n\u003cbr\u003e\n\u003cbr\u003e\n\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n","brand":"Dover Publications","offers":[{"title":"Default Title","offer_id":46431150768259,"sku":"SPTM-9780486422572","price":19.95,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0564\/6830\/8099\/files\/9780486422572_spiral.png?v=1769660377","url":"https:\/\/sebink.com\/products\/combinatorics-of-finite-sets","provider":"Sebink","version":"1.0","type":"link"}