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The kernel of the adjacency matrix of a rectangular mesh
Carlos Tomei, Tania Vieira
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 k…
A special tiling of the rectangle
Carlos Tomei, Tania Vieira
We count tilings of a rectangle of integer sides m-1 and n-1 by a special set of tiles. The result is obtained fron the study of the kernel of the adjacency matrix of an n x n rect…
An overview of domino and lozenge tilings
Nicolau C. Saldanha, Carlos Tomei
We consider tilings of quadriculated regions by dominoes and of triangulated regions by lozenges. We present an overview of results concerning tileability, enumeration and the stru…
Spectra of semi-regular polytopes
Nicolau C. Saldanha, Carlos Tomei
We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the…