Combinatorics: Set Systems, Hypergraphs, Families of Vectors by Béla Bollobás

By Béla Bollobás

Combinatorics is a publication whose major subject matter is the examine of subsets of a finite set. It supplies a radical grounding within the theories of set platforms and hypergraphs, whereas offering an advent to matroids, designs, combinatorial likelihood and Ramsey idea for limitless units. The gem stones of the idea are emphasised: attractive effects with dependent proofs. The booklet built from a direction at Louisiana kingdom collage and combines a cautious presentation with the casual variety of these lectures. it may be an incredible textual content for senior undergraduates and starting graduates.

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Additional resources for Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Probabilistic Combinatorics

Example text

L,where L is an integer 2: 2,which has the following two properties: 1) All intervals Av have the same length bv - a// == w, and their open kernels are pairwise disjoint. 2) The initial elements a v , // == 1, ... , L, form an arithmetic progression with al < .... < aL. Because of 1) the same then also holds for the final elements bv , v == 1, ... ,n. Again we call the step-length of the arithmetic progression {aI, ... , aL} also the step-length of the arithmetic interval sequence. - the shrink factor of {AI, ...

Althofer et al. ), Numbers, Information and Complexity, 45-74. © 2000 Kluwer Academic Publishers. 46 of subsets of a finite set. The ingenious, relatively elementary methods were elaborated by Ahlswede and Khachatrian in several papers [2, 1, 4, 3]. Our aim is to provide a unifying approach such that most of the results are covered. Since Erdos, Ko and Rado [11] have initiated the study of such problems in the thirties many results were obtained by several authors. Here we cite only the recent papers which are related to the new AK-methods.

A 76, 1996, 99-107. [4) E. Harzheim, "Weakly arithmetic progressions in sets of natural numbers", Discrete Math. 89, 1991, 105-107. [5) E. Harzheim, "On weakly arithmetic progressions", Discrete Math. 138, 1995, 255-260. B. Nathanson, "Arithmetic progressions contained in sequences with bounded gaps", Ganad. Math. Bull 23, 1980, 491-493. R. Rabung, "On applications of van der Waerden's theorem", Math. Mag. 48, 1975, 142-148. [8) A. Sarkozy, "Some metric problems in the additive number theory I", Annales Univ.

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