Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schutzenberger, Macdonald, and others. We give an explicit combinatorialâ€¦ (More)

We study a sequence, c, which encodes the lengths of blocks in the Thue-Morse sequence. In particular, we show that the generating function for c is a simple product. Consider the sequence c : c0;â€¦ (More)

In 1961, P.W. Kasteleyn enumerated the domino tilings of a 2n Ã— 2n chessboard. His answer was always a square or double a square (we call such a number "squarish"), but he did not provide aâ€¦ (More)

We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. Weâ€¦ (More)

We show that neither the 3-ball nor the solid torus admits a triangulation in which (i) every vertex is on the boundary, and (ii) every tetrahedron has exactly one triangle on the boundary. (Suchâ€¦ (More)