14 citations · 87 across the 38 of their papers we have counts for
6 papers · 1 filter
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…
Parametrization by polytopes of intersections of orbits by conjugation
Ricardo S. Leite, Carlos Tomei
Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_…
Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators
Dan Burghelea, Nicolau C. Saldanha, Carlos Tomei
We consider the nonlinear Sturm-Liouville differential operator for , a Sobolev space of functions satisfying Dirichlet boundary condition…
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…
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
H. Bueno, C. Tomei
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Diric…
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…