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Mathematical Case Studies: Finite Combinatorics

By Rob Arthan


This document presents some definitions and theorems from elementary finite combinatorics. The definitions include a “fold ” operator for finite sets and the operation that sums a real-valued function on a finite indexed set. The theorems include: more facts about finiteness and the size of finite sets; algebraic properties of indexed sums; induction over finitely-supported functions; the inclusion/exclusion principle; the binomial coefficients and their basic properties, including the formula for the number of combinations and the binomial theorem.

Year: 2006
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