On 3-harness weaving: cataloging designs generated by fundamental blocks having distinct rows and columns.
On a tiling scheme from M. C. Escher.
On the algebraic form of Keller's conjecture
On the area discrepancy of triangulations of squares and trapezoids.
On the Fundamental Group of self-affine plane Tiles
Let be an expanding matrix, a set with elements and define via the set equation . If the two-dimensional Lebesgue measure of is positive we call a self-affine plane tile. In the present paper we are concerned with topological properties of . We show that the fundamental group of is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of . Furthermore, we give a short proof of the fact that the closure of each component of is a locally...
On the norms of the random walks on planar graphs
We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.
On the number of fully packed loop configurations with a fixed associated matching.
On the sequence A079500 and its combinatorial interpretations.
On Translating One Polyomino To Tile the Plane.