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| Title: | Hyperpfaffians in Algebraic Combinatorics |
| Authors: | Redelmeier, Daniel |
| Keywords: | Mathematics
Hyperpfaffian
Pfaffian
Combinatorics |
| Approved Date: | 2006 |
| Date Submitted: | 2006 |
| Abstract: | The pfaffian is a classical tool which can be regarded as a generalization of the determinant. The hyperpfaffian, which was introduced by Barvinok, generalizes the pfaffian to higher dimension. This was further developed by Luque, Thibon and Abdesselam. There are several non-equivalent definitions for the hyperpfaffian, which are discussed in the introduction of this thesis. Following this we examine the extension of the Matrix-Tree theorem to the Hyperpfaffian-Cactus theorem by Abdesselam, proving it without the use of the Grassman-Berezin Calculus and with the new terminology of the non-uniform hyperpfaffian. Next we look at the extension of pfaffian orientations for counting matchings on graphs to hyperpfaffian orientations for counting matchings on hypergraphs. Finally pfaffian rings and ideal s are extended to hyperpfaffian rings and ideals, but we show that under reason able assumptions the algebra with straightening law structure of these rings cannot be extended. |
| Department: | Combinatorics and Optimization |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/1055 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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