Boros and Füredi (for d = 2) and Bárány (for arbitrary d) proved that there exists a positive real number cd such that for every set P of n points in R d in general position, there exists a point of R contained in at least cd ( n d+1 ) d-simplices with vertices at the points of P . Gromov improved the known lower bound on cd by topological means. Using methods from extremal combinatorics, we im...

Section 1 summarizes my accomplishments and ongoing research program in the field of geometric Ramsey theory, specifically on finding geometric configurations in sets of positive density in R. Section 2 summarizes my work in arithmetic combinatorics, specifically on single recurrence problems such as finding polynomial configurations in sets of positive density and related problems in diophanti...

Combinatorics, Probability and Computing / Volume 20 / Issue 04 / July 2011, pp 631 640 DOI: 10.1017/S0963548311000204, Published online: 31 May 2011 Link to this article: http://journals.cambridge.org/abstract_S0963548311000204 How to cite this article: BAOGANG XU and XINGXING YU (2011). Better Bounds for k-Partitions of Graphs. Combinatorics, Probability and Computing, 20, pp 631-640 doi:10.1...

We provide a survey of results concerning both the direct and inverse problems to the Cauchy-Davenport theorem and Erdős-Heilbronn problem in Additive Combinatorics. We formulate a conjecture concerning the inverse Erdős-Heilbronn problem in nonabelian groups. We prove an inverse to the Dias da Silva-Hamidoune Theorem to Z/nZ where n is composite, and we generalize this result for nonabelian gr...

a and the CIP team.

We present the mathematical work of Yahya Ould Hamidoune, emphasizing his main achievements, notably in graph theory and additive combinatorics.