The Friendship Theorem and Minimax Theorems

Details The Friendship Theorem and Minimax Theorems The Friendship Theorem and Minimax Theorems

2005-03-25

arxiv.org/abs/math/0503578v1

Mathematics

General Mathematics

8 pages

Scientific paper

We propose a generalization of Halls marriage theorem. The generalization given here provides a necessary sufficient condition for arranging a successful friendship among n number of k sets. We define multimatrix, multideterminant, multideterminantal monomials, and show that the existence of a nonzero multideterminantal monomial implies the desired existence of a successful friendship. Every nonzero multideterminantal monomial represents a possible way to achieve a successful friendship. A generalization of Mengers theorem and that of some minimax theorems is stated.

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