In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer n≥3, we define e(n) to be the minimum positive integer such that an ...
Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...
The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...
Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...
Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and L2 distances between such curves. In partic ...
IEEE Institute of Electrical and Electronics Engineers2016
A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...
For any positive integers n≥3,r≥1 we present formulae for the number of irreducible polynomials of degree n over the finite field F2r where the coefficients of xn−1, xn−2 and xn−3 are zero. Our proofs involve coun ...
