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- Carlos Tomei, Tania Vieira
- Discrete & Computational Geometry
- 2002

Given an m × n rectangular mesh, its adjacency matrix A, having only integer entries, may be interpreted as a map between vector spaces over an arbitrary field K. We describe the kernel of A: it is a direct sum of two natural subspaces whose dimensions are equal to ⌈c/2⌉ and ⌊c/2⌋, where c = gcd(m + 1, n + 1) − 1. We show that there are bases to both vector… (More)

- Carlos Tomei, Tania Vieira
- 2001

We count tilings of a rectangle of integer sides m − 1 and n − 1 by a special set of tiles. The result is obtained from the study of the kernel of the adjacency matrix of an m × n rectangular subgraph in Z × Z.

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