volume 28, issue 3, P411-425 2002
DOI: 10.1007/s00454-002-2819-z
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Abstract: AbstractGiven 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 spaces, with entries equal to 0, 1 and −1. When K = Z/(2), the kernel elements of these subspaces are described by rectangular tilings of a specia…

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