# Combinatorics of Finite Sets

## Anderson, Ian

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Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed.

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Contenuti:

Notation 1. Introduction and Sperner's theorem 1.1 A simple intersection result 1.2 Sperner's theorem 1.3 A theorem of Bollobás 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 Erdös-Ko-Rado theorem 5.1 The EKR theorem 5.2 Generalizations of EKR 5.3 Intersecting antichains 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 Chvátal's conjecture Exercises 6 7. The Kruskal-Katona theorem 7.1 Order relations on subsets 7.2 The l-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 Lindström 9.2 Some corollaries 9.3 A minimization problem in coding theory 9.4 Uniqueness of a 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

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## 1.Combinatorics of Finite Sets Format: Trade Paper

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ISBN 10: 0486422577 ISBN 13: 9780486422572
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Descrizione libro Dover Publishers. Condizione libro: New. Brand New. Codice libro della libreria 0486422577

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## 2.Combinatorics of Finite Sets (Dover Books on Mathematics)

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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486422577 New Condition. Codice libro della libreria 329-474C-F696

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## 3.Combination of Finite Sets

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Descrizione libro Dover Publications Inc., 2003. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780486422572

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## 4.Combinatorics of Finite Sets

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Descrizione libro Paperback. Condizione libro: New. This item is printed on demand. Item doesn't include CD/DVD. Codice libro della libreria 6332251

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## 5.Combination of Finite Sets (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2011. Paperback. Condizione libro: New. 214 x 136 mm. Language: English . Brand New Book ***** Print on Demand *****.Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k -saturated chain partitions of general partially ordered sets. Connections with Dilworth s theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. An excellent text for a topics course in discrete mathematics. -- Bulletin of the American Mathematical Society. Codice libro della libreria APC9780486422572

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## 6.Combination of Finite Sets (Paperback)

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Descrizione libro Dover Publications Inc., United States, 2011. Paperback. Condizione libro: New. 214 x 136 mm. Language: English . Brand New Book ***** Print on Demand *****. Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k -saturated chain partitions of general partially ordered sets. Connections with Dilworth s theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. An excellent text for a topics course in discrete mathematics. -- Bulletin of the American Mathematical Society. Codice libro della libreria APC9780486422572

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## 7.Combinatorics of Finite Sets (Dover Books on Mathematics)

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ISBN 10: 0486422577 ISBN 13: 9780486422572
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Descrizione libro Dover Publications, 2011. Paperback. Condizione libro: New. Codice libro della libreria INGM9780486422572

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## 8.Combinatorics of Finite Sets (Dover Books on Mathematics)

Editore: Dover Publications (2011)
ISBN 10: 0486422577 ISBN 13: 9780486422572
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Descrizione libro Dover Publications, 2011. Condizione libro: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Notation1. Introduction and Sperner's theorem1.1 A simple intersection result1.2 Sperner's theorem1.3 A theorem of BollobsExercises 12. Normalized matchings and rank numbers2.1 Sperner's proof2.2 Systems of distinct representatives2.3 LYM inequalities and the normalized matching property2.4 Rank numbers: some examplesExercises 23. Symmetric chains3.1 Symmetric chain decompositions3.2 Dilworth's theorem3.3 Symmetric chains for sets3.4 Applications3.5 Nested Chains3.6 Posets with symmetric chain decompositionsExercises 34. Rank numbers for multisets4.1 Unimodality and log concavity4.2 The normalized matching property4.3 The largest size of a rank numberExercises 45. Intersecting systems and the Erds-Ko-Rado theorem5.1 The EKR theorem5.2 Generalizations of EKR5.3 Intersecting antichains with large members5.4 A probability application of EKR5.5 Theorems of Milner and Katona5.6 Some results related to the EKR theoremExercises 56. Ideals and a lemma of Kleitman6.1 Kleitman's lemma6.2 The Ahlswede-Daykin inequality6.3 Applications of the FKG inequality to probability theory6.4 Chvtal's conjectureExercises 67. The Kruskal-Katona theorem7.1 Order relations on subsets7.2 The l-binomial representation of a number7.3 The Kruskal-Katona theorem7.4 Some easy consequences of Kruskal-Katona7.5 CompressionExercises 78. Antichains8.1 Squashed antichains8.2 Using squashed antichains8.3 Parameters of intersecting antichainsExercises 89. The generalized Macaulay theorem for multisets9.1 The theorem of Clements and Lindstrm9.2 Some corollaries9.3 A minimization problem in coding theory9.4 Uniqueness of a maximum-sized antichains in multisetsExercises 910. Theorems for multisets10.1 Intersecting families10.2 Antichains in multisets10.3 Intersecting antichainsExercises 1011. The Littlewood-Offord problem11.1 Early results11.2 M-part Sperner theorems11.3 Littlewood-Offord resultsExercises 1112. Miscellaneous methods12.1 The duality theorem of linear programming12.2 Graph-theoretic methods12.3 Using network flowExercises 1213. Lattices of antichains and saturated chain partitions13.1 Antichains13.2 Maximum-sized antichains13.3 Saturated chain partitions13.4 The lattice of k-unionsExercises 13Hints and solutions; References; Index. Codice libro della libreria ABE_book_new_0486422577

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## 9.Combinatorics of Finite Sets (Dover Books on Mathematics)

Editore: Dover Publications (2011)
ISBN 10: 0486422577 ISBN 13: 9780486422572
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Descrizione libro Dover Publications, 2011. Paperback. Condizione libro: New. book. Codice libro della libreria 0486422577

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## 10.Combination of Finite Sets

Editore: Dover Publications Inc. (2003)
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Descrizione libro Dover Publications Inc., 2003. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780486422572

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