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Pfaffians, involutions, and Schur functions

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Our objective is to exhibit several facts concerning Pfaffians, and their relationship to Schur functions. We adopt the combinatorial point of view that the Pfaffian is a weighted generating function for perfect matchings, in analogy with the definition of the determinant as a weighted generating function for permutations.

Author(s): Thomas Scott Sundquist
Publisher: University of Minnesota
Year: 1992

Language: English
Commentary: PhD thesis at University of Minnesota

0. Introduction 1
1. Some Pfaffian evaluations 3
2. Symmetric functions 23
3. More on tournaments 43
4. Quotients of specialized Schur functions 53
Bibliography 70