We prove lower bounds for the direct sum problem for two-party bounded error randomised multipleround communication protocols. Our proofs use the notion of information cost of a p...
We investigate the relationship between geometric thickness and the thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity tw...
In this paper we ask the question whether the extended Frege proof system EF satisfies a weak version of the deduction theorem. We prove that if this is the case, then complete dis...
The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity A(x) := n=0 a(n)xn = n=1 (1 - xn )-p(n) satisfies t...
: We prove two extensions of the Hales-Jewett coloring theorem. The first is a polynomial version of a finitary case of Furstenberg and Katznelson's multiparameter elaboration...