Titlebook: Extremal Combinatorics; With Applications in Stasys Jukna Textbook 2011Latest edition Springer-Verlag Berlin Heidelberg 2011 Combinatorics.

ingrate

https://doi.org/10.1057/9781403907301amily reflects some kind of “dependence” between them. In this chapter we will study the weakest kind of this dependence – the members are required to be non-disjoint. A family is . if any two of its sets have a non-empty intersection.

Ceramic

https://doi.org/10.1007/978-94-011-4463-6elation < between its elements which is transitive and antysymmetric: if .<. and .<. then .<., but .<. and .<. cannot both hold. We write .≤. if .<. or .=.. Elements . and . are . if either .≤. or .≤. (or both) hold.

figment

municipality

裁决

Cursory

Intersecting Familiesamily reflects some kind of “dependence” between them. In this chapter we will study the weakest kind of this dependence – the members are required to be non-disjoint. A family is . if any two of its sets have a non-empty intersection.

canonical

Chains and Antichainselation < between its elements which is transitive and antysymmetric: if .<. and .<. then .<., but .<. and .<. cannot both hold. We write .≤. if .<. or .=.. Elements . and . are . if either .≤. or .≤. (or both) hold.

执

Density and Universalityoperty play an important role: . Such sets are called (.,.)-.. If the same holds not for all but only for . subset . of . indices, then . is called (.,.)-.. The maximal number ., for which . is (.,.)-dense, is also known as the . of ..

Fibroid

Eigenvalues and Graph Expansionmize algorithms as well as to construct good error-correcting codes. Basically, an expander has the property that every subset of its vertices has a large set of neighbors. This particularly implies that any pair of vertices is connected by a short path.

cavity