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VOL. 59 | 2010 Computation of principal $\mathcal{A}$-determinants through dimer dynamics
Jan Stienstra

Editor(s) Masa-Hiko Saito, Shinobu Hosono, Kōta Yoshioka

## Abstract

$\mathcal{A}$ is a set of $N$ vectors in $\mathbb{Z}^{N-2}$ situated in a hyperplane not through 0 and spanning $\mathbb{Z}^{N-2}$ over $\mathbb{Z}$. Gulotta's algorithm [4] constructs from $\mathcal{A}$ a dimer model. $\mathcal{A}$ theorem in [6] states that the principal $\mathcal{A}$-determinant equals the determinant of (a suitable form of) the Kasteleyn matrix of that dimer model. In the present note we translate Gulotta's pictorial description of the algorithm into matrix operations. As a result one obtains an algorithm for computing the principal $\mathcal{A}$-determinant, which is much faster than the algorithm in [5].

## Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1215.82012
MathSciNet: MR2683214

Digital Object Identifier: 10.2969/aspm/05910349

Subjects:
Primary: 82B20
Secondary: 33C70