We prove that tree isomorphism is not expressible in the language (FO + TC + COUNT). This is surprising since in the presence of ordering the language captures NL, whereas tree is...
We address a question posed by Sibley and Wagon. They proved that rhombic Penrose tilings in the plane can be 3colored, but a key lemma of their proof fails in the natural 3D gene...
We study the computation of rotation-invariant similarity measures of convex polyhedra, based on Minkowski's theory of mixed volumes. To compute the similarity measure, a (mix...
We give combinatorial proofs of the formulas for the number of multichains in the k-divisible noncrossing partitions of classical types with certain conditions on the rank and the ...
In this paper we show a reduction from the Unique Games problem to the problem of approximating MAX-CUT to within a factor of GW + , for all > 0; here GW .878567 denotes the a...
Subhash Khot, Guy Kindler, Elchanan Mossel, Ryan O...