Shalom Eliahou

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Let D n be the dihedral group of order 2n. For all integers r, s such that 1 ≤ r, s ≤ 2n, we give an explicit upper bound for the minimal size µ D n (r, s) = min |A · B| of sumsets (product sets) A · B, where A and B range over all subsets of D n of cardinality r and s respectively. It is shown by construction that µ D n (r, s) is bounded above by the known(More)
Nested Monte-Carlo Search (NMC) and Nested Rollout Policy Adaptation (NRPA) are Monte-Carlo tree search algorithms that have proved their efficiency at solving one-player game problems, such as morpion solitaire or sudoku 16x16, showing that these heuristics could potentially be applied to constraint problems. In the field of Ramsey theory, the weak Schur(More)
The Cauchy-Davenport theorem states that, if p is prime and A, B are nonempty subsets of cardinality r, s in Z/pZ, the cardinality of the sumset A + B = {a + b | a ∈ A, b ∈ B} is bounded below by min(r + s − 1, p); moreover, this lower bound is sharp. Natural extensions of this result consist in determining, for each group G and positive integers r, s ≤(More)