The mechanics of shuffle products and their siblings

We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name $\varphi$-shuffle products. Our paper is dedicated to a study of the latter class, from a combinatorial standpoint. We consider first how to extend Radford's theorem to the products in that class, then how to construct their bi-algebras. As some conditions are necessary do carry that out, we study them closely and simplify them so that they can be seen directly from the definition of the product. We eventually test these conditions on the products mentioned above

The heparin-Ca2+ interaction: metal influence characterized by MS/MS and UVPD experiments

Communication par afficheInternational audienc

The contrivances of shuffle products and their siblings

In order to calculate and effectively represent special functions on the one hand, work on the other hand, we analyze a class of mixed product. We analyze in particular how to extend the maximum theorem of Radford and compare its applicability to pre-mentioned product

Heparin-like disaccharides: effect of metallic complexation in fragmentation pathways as characterized by MS/MS and UVPD experiments

Communication par afficheNational audienc

Bounds for Completely Decomposable Jacobians

A curve over the eld of two elements with completely decomposable Jacobian is shown to have at most six rational points and genus at most 26. The previous upper bound for the genus was 145

Jacobiennes et cryptographie

L'objectif premier de cette thèse est d'étudier le problème du logarithme discret dans des groupes constitués de jacobiennes généralisées de courbes irréductibles non singulières. Nous donnons tout d'abord un état de l'art de ce problème et de ses diverses attaques connues. Nous étudions ensuite les jacobiennes généralisées et exhibons leurs liens avec des groupes de classes d'ordres. Nous reportons alors nos visées cryptographiques à ces groupes de classes : nous donnons des applications cryptographiques utilisant des corps quadratiques, et nous utilisons les groupes de classes pour construire des exemples permettant de tester les attaques connues. Nous finissons par l'étude des courbes utilisées. Nous donnons des majorations du genre et du nombre de points rationnels de certaines de ces courbes, ainsi que des conditions permettant de localiser leurs angles de Frobenius.LIMOGES-BU Sciences (870852109) / SudocSudocFranceF

Combinatorial study of colored Hurwitz polyzêtas

A combinatorial study discloses two surjective morphisms between generalized shuffle algebras and algebras generated by the colored Hurwitz polyzêtas. The combinatorial aspects of the products and co-products involved in these algebras will be examined.