Christophe Tollu

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We investigate the expressive power of various extensions of rst-order, inductive, and innnitary logic with counting quantiiers. We consider in particular a LOGSPACE extension of rst-order logic, and a PTIME extension of xpoint logic with counters. Counting is a fundamental tool of algorithms. It is essential in the case of unordered structures. Our aim is(More)
The framework used to prove the multiplicative law deformation of the algebra of Feynman-Bender diagrams is a twisted shifted dual law (in fact, twice). We give here a clear interpretation of its two parameters. The crossing parameter is a deformation of the tensor structure whereas the superposition parameters is a perturbation of the shuffle coproduct of(More)
We investigate two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender’s QFT (quantum field theory) of partitions. We end by exploring possibilities to construct noncommutative analogues.(More)
G. H. E. DUCHAMP∗,§, J.-G. LUQUE†,¶, J.-C. NOVELLI‡,‖, C. TOLLU∗,∗∗ and F. TOUMAZET‡,†† ∗Institut Galilée, LIPN, CNRS UMR 7030 99, Avenue J.-B. Clement, F-93430 Villetaneuse, France †LITIS, Université de Rouen; Avenue de l’université 76801 Saint Étienne du Rouvray, France ‡Université Paris-Est, Institut Gaspard Monge 5 Boulevard Descartes, Champs-Sur-Marne(More)