14 citations · 87 across the 38 of their papers we have counts for
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Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix
Nicolau C. Saldanha, Carlos Tomei
We define cut-and-paste, a construction which, given a quadriculated disk obtains a disjoint union of quadriculated disks of smaller total area. We provide two examples of the use…
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…
Arithmetic properties of the adjacency matrix of quadriculated disks
Nicolau C. Saldanha, Carlos Tomei
Let be a bicolored quadriculated disk with black-to-white matrix . We show how to factor , where and are lower and upper triangular matrices, $\ti…
Two results on tilings of quadriculated annuli
Nicolau C. Saldanha, Carlos Tomei
We provide a more informal explanation of two results in our manuscript "Tilings of quadriculated annuli". Tilings of a quadriculated annulus are counted according to volume (i…
Tilings of quadriculated annuli
Nicolau C. Saldanha, Carlos Tomei
Tilings of a quadriculated annulus A are counted according to volume (in the formal variable q) and flux (in p). We consider algebraic properties of the resulting generating functi…