4 citations · 9 across the 4 of their papers we have counts for
5 papers
No skew branes on non-degenerate hyperquadrics
Ji-Ping Sha, Bruce Solomon
We show that non-degenerate hyperquadrics in R^{n+2} admit no skew branes. Stated more traditionally, a compact codimension-one immersed submanifold of a non-degenerate hyperquadri…
Large-determinant sign matrices of order 4k+1
William P. Orrick, Bruce Solomon
The Hadamard maximal determinant problem asks for the largest n-by-n determinant with entries in {+1,-1}. When n is congruent to 1 (mod 4), the maximal excess construction of Farma…
New lower bounds for the maximal determinant problem
William P. Orrick, Bruce Solomon, Roland Dowdeswell +1
We report new world records for the maximal determinant of an n-by-n matrix with entries +/-1. Using various techniques, we beat existing records for n=22, 23, 27, 29, 31, 33, 34,…
Projecting (n-1)-cycles to zero on hyperplanes in R^{n+1}
Bruce Solomon
The projection of a compact oriented submanifold M^{n-1} in R^{n+1} on a hyperplane P^{n} can fail to bound any region in P. We call this ``projecting to zero.'' Example: The equat…
Skew loops and quadric surfaces
Mohammad Ghomi, Bruce Solomon
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the…