IAS/PCMI Summer Session 2000 Clay Mathematics Undergraduate Program Advanced Course on Computational Complexity Lecture 13: Polynomial-Size Frege Proofs of the Pigeonhole Principle
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چکیده
The pigeonhole principle states that there is no one-to-one function from a set of size n to a set of size n − 1. In other words, if n pigeons are put into n − 1 holes, then at least one hole will be occupied by more than one pigeon. This simple fact has an astonishing variety of applications in mathematics. It also corresponds to a tautology that has been used extensively in the study of the complexity of proof systems.
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