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Determinants, Permanents, and the Enumeration of Forest-partitions

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Author(s): Adam H. Berliner
Series: PhD thesis at University of Wisconsin-Madison
Year: 2009

Language: English

Abstract i
Acknowledgements ii
1 Overview 1
1.1 Enumeration of Forest-partitions 1
1.2 Determinants and Permanents 2
2 Forest-Partitions 5
2.1 Integer Partitions and Graphs 5
2.2 Enumeration of Forest-Partitions 11
3 The Dodgson/Muir Determinantal Identity 26
3.1 Dodgson's Rule and Muir's Law 26
3.2 Combinatorial Proof of the Dodgson/Muir Identity 29
4 Calculating Permanents via Determinants 38
4.1 Convertible Matrices 38
4.2 m-Convertible Matrices 45
4.3 General m-Convertibility and J n 52
Bibliography 68