Arithmetic properties of the adjacency matrix of quadriculated disks

Abstract

Let $\Delta$ be a bicolored quadriculated disk with black-to-white matrix $B_{\Delta }$. We show how to factor $B_{\Delta }=L\tilde{D}U$, where $L$ and $U$ are lower and upper triangular matrices, $\tilde{D}$ is obtained from a larger identity matrix by removing rows and columns and all entries of $L$, $\tilde{D}$ and $U$ are equal to 0, 1 or -1.

12 pages, 9 figures

References in corpus (1)

• Alternating sign matrices and domino tilings

Cited by in corpus (1)

• The kernel of the adjacency matrix of a rectangular mesh