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**Combinatorics** is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and is in particular concerned with "counting" the objects in those collections (*enumerative combinatorics*) and with deciding whether certain "optimal" objects exist (*extremal combinatorics*). One of the most prominent combinatorialists of recent times was Gian-Carlo Rota, who helped formalize the subject beginning in the 1960s. The problem-solver Paul Erdős worked mainly on extremal questions. The study of how to count objects is sometimes thought of separately as the field of enumeration.