Author

Ran JiFollow

Date

2013

Department or Program

Mathematics

Primary Wellesley Thesis Advisor

Andrew C. Schultz

Abstract

Kuperberg proved the conjecture on the number of alternating sign matrices (ASMs) of rank n using its partition function, found through its corresponding ice model. He went on to discover subclasses of ASMs with specific symmetry properties and their corresponding ice models, and was able to enumerate these matrices by making a connection between partition functions and x-enumerations. Using similar methods, Razumov and Stroganov enumerated the class of half-turn symmetric alternating sign matrices of odd order by connecting its partition function to partition functions whose explicit formulas are known. We introduce two new classes of half-turn symmetric matrices, C-alt and D. For both the C-alt and D matrices, we prove symmetry properties and recursive formulas for their partition functions. For the C-alt matrices, we also find lead coefficients on specific lead terms in its partition function.

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