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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)

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