The kernel of the adjacency matrix of a rectangular mesh
| dc.creator | Tomei, Carlos | |
| dc.creator | Vieira, Tania | |
| dc.date | 2002-01-22 | |
| dc.date.accessioned | 2026-07-07T04:46:02Z | |
| dc.date.available | 2026-07-07T04:46:02Z | |
| dc.description | Given an m x 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 $\lceil c/2 \rceil$ and $\lfloor c/2 \rfloor$, 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 special kind. As a corollary, we count the number of tilings of a rectangle of integer sides with a specified set of tiles. | |
| dc.description | 15 pages, 17 figures | |
| dc.identifier | https://arxiv.org/abs/math/0201211 | |
| dc.identifier | http://arxiv.org/abs/math/0201211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63177 | |
| dc.subject | Combinatorics | |
| dc.subject | 05B45; 05C50 | |
| dc.title | The kernel of the adjacency matrix of a rectangular mesh | |
| dc.type | text |