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Proofs and confirmations

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Author(s): David Bressoud
Publisher: Cambridge
Year: 1999

Language: English

Cover
Title page
Preface
1 The Conjecture
1.1 How many are there?
1.2 Connections to plane partitions
1.3 Descending plane partitions
2 Fundamental Structures
2.1 Generating functions
2.2 Partitions
2.3 Recursive formulre
2.4 Determinants
3 Lattice Paths and Plane Partitions
3.1 Lattice paths
3.2 Inversion numbers
3.3 Plane partitions
3.4 Cyclically symmetric plane partitions
3.5 Dodgson's algorithm
4 Symmetric Functions
4.1 Schur functions
4.2 Semistandard tableaux
4.3 Proof of the MacMahon conjecture
5 Hypergeometric Series
5.1 Mills, Robbins, and Rumsey's bright idea
5.2 Identities for hypergeometric series
5.3 Proof of the Macdonald conjecture
6 Explorations
6.1 Charting the territory
6.2 Totally symmetric self-complementary plane partitions
6.3 Proof of the ASM conjecture
7 Square Ice
7.1 Insights from statistical mechanics
7.2 Baxter's triangle-to-triangle relation
7.3 Proof of the refined ASM conjecture
7.4 Forward
Bibliography
Index of Notation
General Index
Photos (mediocre)