Combinatorics of Finite Sets

Ian Anderson (Autor)

Buch | Softcover

264 Seiten

1989 | New edition
Clarendon Press (Verlag)
978-0-19-853379-5 (ISBN)

Infos

It is the aim of this book to provide a coherent and up-to-date account of the basic methods and results of the combinatorial study of finite set systems. From its origins in a 1928 theorem of Sperner, this subject has become a lively area of combinatorial research, unified by the gradual discovery of structural insights and widely applicable proof techniques. Much of the material in the book concerns subsets of a set, but there are chapters dealing with more general partially ordered sets: for example, the Clements-Lindstr on extension of the Kruscal-Katona theorem to multisets is discussed, 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 presented. Each chapter ends with a collection of exercises for which outline solutions are provided, and there is an extensive bibliography.

Inhalt

Introduction and Sperner's theorem; Normalized matchings and rank numbers; Symmetric chains; Rank numbers for multisets; Intersecting systems and the Erd "os-Ko-Rado theorem; Ideals and a lemma of Kleitman; The Kruskal-Katona theorem; Antichains; The generalized Macaulay theorem for multisets; Theorems for multisets; The Littlewood-Offord problem; Miscellaneous methods; Lattices of antichains and saturated chain partitions; Hints and solutions.

Produkt-Details

• Zusatzinfo: bibliography
• Verlagsort: Oxford
• Sprache: englisch
• Maße: 155 x 230 mm
• Gewicht: 435 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• ISBN-10: 0-19-853379-9 / 0198533799
• ISBN-13: 978-0-19-853379-5 / 9780198533795
• Zustand: Neuware