Arithmetic properties of the adjacency matrix of quadriculated disks

Details Arithmetic properties of the adjacency matrix of quadriculated disks Arithmetic properties of the adjacency matrix of quadriculated disks

2001-07-23

arxiv.org/abs/math/0107162v2

Mathematics

Combinatorics

12 pages, 9 figures

Scientific paper

Let $\Delta$ be a bicolored quadriculated disk with black-to-white matrix
$B_\Delta$. We show how to factor $B_\Delta = L\tilde DU$, 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.

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