We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty 'Number on the Forehead' model. Our method is based on the notion of voting polynomial degree of functions and extends the Degree-Discrepancy Lemma in the recent work of Sherstov (STOC'07). ... more >>>

A basic fact in linear algebra is that the image of the curve
$f(x)=(x^1,x^2,x^3,...,x^m)$, say over $C$, is not contained in any
$m-1$ dimensional affine subspace of $C^m$. In other words, the image
of $f$ is not contained in the image of any polynomial-mapping
$G:C^{m-1} ---> C^m$ ... more >>>