Some remarks on barycentric-sum problems over cyclic groups

We derive some new results on the k-th barycentric Olson constants of abelian groups (mainly cyclic). This quantity, for a finite abelian (additive) group (G,+), is defined as the smallest integer l such that each subset A of G with at least l elements contains a subset with k elements {g_1, ..., g_k} satisfying g_1 + ... + g_k = k g_j for some 1 <= j <= k.Comment: to appear in European Journal of Combinatoric

On the structure of subsets of an orderable group with some small doubling properties

The aim of this paper is to present a complete description of the structure of subsets S of an orderable group G satisfying |S^2| = 3|S|-2 and is non-abelian

A new upper bound for the cross number of finite Abelian groups

In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite Abelian group, this upper bound appears to depend only on the rank and on the number of distinct prime divisors of the exponent. The main theorem of this paper allows us, among other consequences, to prove that a classical conjecture concerning the cross and little cross numbers of finite Abelian groups holds asymptotically in at least two different directions.Comment: 21 pages, to appear in Israel Journal of Mathematic

Production et transformation du manioc

De son nom scientifique Manihot esculenta, le manioc est l’une des cultures vivrières les plus cultivées et les plus consommées dans de nombreuses régions du monde. Arbuste de 1 à 4 mètres de hauteur environ, il est cultivé pour ses tubercules et ses feuilles. Les tubercules sont très riches en amidon. Les tiges sont quant à elles utilisées comme matériel de plantation. Consommé tant pour l’alimentation humaine qu’animale, le manioc est très utilisé dans l’industrie alimentaire (pâtisseries, tapioca, pâtes alimentaires, cossettes, …). Avec plus de vingt produits dérivés, le manioc sert également dans l’industrie textile, la production du papier, de colles, d’alcool ou d’amidon