Dans l’étude des fonctions symétriques, la théorie des λ-anneaux est une méthode particulièrement efficace, et pourtant peu utilisée. On trouvera une illustration de cette théorie dans [5]. Le but de cet article est d’en présenter une nouvelle application. Nous considérons le problème suivant : si f est une fonction symétrique et q une indéterminée, quelle est la valeur de f(1, q, q, . . . , q)...

This paper deals with various problems in lattice theory related to the notion of parity. Résumé. Sur les classes de parité. Nous considérons dans cet article divers problèmes de la théorie des réseaux liés à des questions de parité.

— We show how the ideas of Leray (sheaf theory), Grothendieck (derived categories) and Sato (microlocal analysis) lead to the microlocal theory of sheaves which allows one to reduce many problems of linear partial differential equations to problems of microlocal geometry. Moreover, sheaves on Grothendieck topologies are a natural tool to treat growth conditions which appear in Analysis. Résumé ...

We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative prim...

Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this paper, we present the full development of a generation engine by describing the related theory, establishing a mathematical and practical complexity, and exposin...

— In this note we prove the existence of effectively independent instances (with respect to an arbitrary recursively axiomatizable, consistent, intuitively true and sufficiently rich theory) for some well-known undecidable problems including the Emptiness Problem, the Finiteness Problem, the Totality Problem, the Halting Problem and the Post Correspondence Problem. Applications in the Theory of...

We evaluate induced sign characters of Hn(q) at certain elements of Hn(q) and conjecture an interpretation for the resulting polynomials as generating functions for P -tableaux by a certain statistic. Our conjecture relates the quantum chromatic symmetric functions of Shareshian and Wachs to Hn(q) characters. Résumé. Nous évaluons les caractères de signe induits de Hn(q) à certains éléments de ...

This presentation considers the biological and mathematical mechanisms involved in the development from the child to a mathematician and theorizes how individuals grow in different ways over a life-time’s experience. The theory is then used to respond to questions on the long-term teaching and learning of mathematics over the whole curriculum from child to adult. Résumé. Une théorie du développ...

Abstract. Pour une large classe d’équations quasilinéaires elliptiques autonomes sur R , on montre l’existence d’une solution de moindre énergie. On montre aussi que toutes les solutions de moindres énergies ont un signe constant et sont, à une translation près, radiales. For a general class of autonomous quasi-linear elliptic equations on R we prove the existence of a least energy solution and...

Providing a high degree of automation to discharge proof obligations in (fragments of) first-order logic is a crucial activity in many verification efforts. Unfortunately, this is quite a difficult task. On the one hand, reasoning modulo ubiquitous theories (such as lists, arrays, and Presburger arithmetic) is essential. On the other hand, to effectively incorporate this theory specific reasoni...