عنوان

Combinatorics of finite sets

Title Proper

Combinatorics of finite sets

Place of Publication, Distribution, etc.

Mineola, N.Y.

Name of Publisher, Distributor, etc.

Dover Publications

Date of Publication, Distribution, etc.

c2002

Specific Material Designation and Extent of Item

xv, 250 p.

Other Title Information

Dover books on mathematics

Text of Note

" ... 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

Text of Note

Includes bibliographical references )p.241-248( and index

Text of Note

Ian Anderson

Text of Note

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 -- 01. Theorems for multisets -- 01.1 Intersecting families -- 01.2 Antichains in multisets -- 01.3 Intersecting antichains -- Exercises 01 -- 11. The Littlewood-Offord problem -- 11.1 Early results -- 11.2 M-part Sperner theorems -- 11.3 Littlewood-Offord results -- Exercises 11 -- 21. Miscellaneous methods -- 21.1 The duality theorem of linear programming -- 21.2 Graph-theoretic methods -- 21.3 Using network flow -- Exercises 21 -- 31. Lattices of antichains and saturated chain partitions -- 31.1 Antichains -- 31.2 Maximum-sized antichains -- 31.3 Saturated chain partitions -- 31.4 The lattice of k-unions -- Exercises 31 -- Hints and solutions -- References -- Index

Entry Element

، Set theory

Entry Element

، Combinatorial analysis

Class number

Entry Element

Anderson, Ian

Relator Code

AU

TI