We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Ω (√ d t ) for writing an explicit univariate degree-d… (More)

In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s′ with s′ < s, are δ-hyperbolic with δ = O(s). We also show that the… (More)

The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partial derivatives of a… (More)

We call shifted power a polynomial of the form (x− a)e. The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family F of shifted powers are… (More)

This is the nal report of an internship in algebraic complexity. First, we give an introduction to algebraic complexity and we give some motivations for the study of the main model. Then we present… (More)