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The Combinatorial PT-DT Correspondence

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Author(s): Gautam Webb
Series: PhD thesis at University of Oregon
Year: 2021

Language: English

Introduction
Definitions
DT
DT Box Configurations
DT Theory and the Dimer Model
The Condensation Recurrence in DT Theory
PT
Labelled PT Box Configurations
Labelled AB Configurations
The Base AB Configuration
The Labelling Algorithm for AB Configurations
Projection to the Base AB Configuration
PT Theory and the Labelled Double-Dimer Model
Proofs of the Equivalence of the Labelling Algorithms
The Condensation Recurrence in PT Theory
Example
Weights
Modifying the Partition mu
The Diagonal of mu
The Partitions mur and muc
The Partition murc
DT Weights
Weight of Minimal Configuration
Algebraic Simplification
PT Weights
Edge-Weight of Base Double-Dimer Configuration
Algebraic Simplification
REFERENCES CITED