Brève communication. Généralisation des extrapolations polynomiales et rationnelles

Pour une généralisation des systèmes C.A.O : approche et applications

Variétés et fonctions rationnelles

We say that a rational (resp. a subsequential) function tl from a free monoid into another one is in the variety of monoids V if it may realized by some unambiguous (resp. subsequential) transducer whose monoid of transitions is in V. We characterize these functions when V is the variety of aperiodic monoids, and the variety of groups. In the first case, the period of am ’ (15) divides that of ...

Un cadre de modélisation des relations entre les réactions rationnelles et comportementales des agents assistants conversationnels

In order to improve the users’ acceptability of conversational assistant agents (CAA), the agents should be supplied with behavioral models, which in turn interact with their basic rational reasoning process. We present here a flexible modeling framework, dedicated to the study of the relationships between the rational and behavioral reactions of CAA. This framework is then used to support the ...

Sur une Généralisation des Coefficients Binomiaux

We prove a recent conjecture of Lassalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to the fundamental problem of calculating the linearization coefficients for binomial coefficients.

Une généralisation automorphe des nombres de Stirling

Let [n] be theset {1,2, *.. , n> and CT a given permutation in S,, the symmetric group on [n]. The (unsigned) Stirling numbers of the first kind enumerate the permutations on En] with k cycles and those of the second kind give the number partitions of [n] having k blocks. In this paper we compute the number of permutations on [n] with k cycles and the number of partitions on [n] having k blocks...