High Quality Content by WIKIPEDIA articles! In mathematics, Tucker's lemma is a combinatorial analog of the Borsuk–Ulam theorem. ombinatorics is a branch of pure mathematics concerning the study of the enumeration of discrete, finite sets. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics. Aspects of combinatorics include "counting" the objects satisfying certain criteria, deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria as in combinatorial designs and matroid theory, finding "largest", "smallest", or "optimal" objects, and finding algebraic structures these objects may have.

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