Maximal ...-Subgroups of the Symmetric Groups.
Note sur les bases du groupe symétrique.
On a constant of Turán and Erdös
On -analogs of recursions for the number of involutions and prime order elements in symmetric groups.
On the maximal order in and
On the number of permutations arising from a problem in cell-biology.
On the number of rim hook tableaux
Opérades cellulaires et espaces de lacets itérés
L’espace des configurations de points distincts de admet une filtration naturelle qui est induite par les inclusions des dans . Nous caractérisons le type d’homotopie de cette filtration par les propriétés combinatoires d’une structure cellulaire sous-jacente, étroitement liée à la théorie des -opérades de May. Cela donne une approche unifiée des différents modèles combinatoires d’espaces de lacets itérés et redémontre les théorèmes d’approximation de Milgram, Smith et Kashiwabara.
Partition identities with an application to group representation theory.
Phénomène de cutoff pour certaines marches aléatoires sur le groupe symétrique
The main purpose of this paper is to exhibit the cutoff phenomenon, studied by Aldous and Diaconis [AD]. Let denote a transition kernel after k steps and π be a stationary measure. We have to find a critical value for which the total variation norm between and π stays very close to 1 for , and falls rapidly to a value close to 0 for with a fall-off phase much shorter than . According to the work of Diaconis and Shahshahani [DS], one can naturally conjecture, for a conjugacy class with...
Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers
If G is a group then the abelian subgroup spectrum of G is defined to be the set of all κ such that there is a maximal abelian subgroup of G of size κ. The cardinal invariant A(G) is defined to be the least uncountable cardinal in the abelian subgroup spectrum of G. The value of A(G) is examined for various groups G which are quotients of certain permutation groups on the integers. An important special case, to which much of the paper is devoted, is the quotient of the full symmetric group by the...
Presentation of the singular part of the Brauer monoid
We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above.
Pseudo-galois Extensions of Boolean Algebras
Quelques propriétés d'une certaine classe d'opérateurs définis sur les groupes symétriques (fixateurs et biinvodécompositions)
Recognition by the set of element orders of symmetric groups of degree and for prime .
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
Sur l'art de sonner les cloches
Sur le groupe de Galois d'un polynôme dont les coefficients sont indépendants.
Sur le rapport anharmonique
Symmetric and permutational generating set of the groups and using and an element of order .