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

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The Polynomial MethodThis method is based on various extensions of the following basic fact about univariate (single-variable) polynomials —known as the “factor theorem”—to the case of multivariate polynomials, that is, polynomials on many variables:

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https://doi.org/10.1007/978-3-8349-9920-7e pigeonhole principle states the following: . Its truth is easy to verify: if every class receives at most . objects, then a total of at most . objects have been distributed. To see that the result is best possible, observe that a set with at most . points can be divided into . groups with at most

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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.

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Hadi Tolga G?ksidan,Erkan Erdil,Bar?? ?akmurmize 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.

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