We prove that there are only finitely many conjugacy classes of arithmetic maximal hyperbolic reflection groups.

of finite symmetric groups.

For a subset S of a finite ordered set P , let S ↑ = {x ∈ P : x ≥ s for some s ∈ S} and S ↓ = {x ∈ P : x ≤ s for some s ∈ S}. For a maximal antichain A of P , let s(A) = max A=U∪D |U ↑ | + |D↓ | |P | , the maximum taken over all partitions U ∪ D of A, and sk(P ) = min A∈A(P ),|A|=k s(A) where we assume P contains at least one maximal antichain of k elements. Finally, for a class C of finite ord...

We give a formula for the character of the representation of the Weyl group Sn on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SLn, with respect to the action of the centre. As a consequence, we find that this representation is induced from a cohomology representation of a wreath product subgroup.

We introduce in this paper an agent model based on coherence theory. We give a formalization of Thagard’s theory on coherence and use it to explain the reasoning process of an intentional agent that permits the agent to drop beliefs or to violate norms in order to keep a maximal state of coherence. The architecture is illustrated in the paper and a discussion on the possible use of this approac...

We build on work of Boris Pittel [5] concerning the number of t-tuples of partitions whose meet (join) is the minimal (maximal) element in the lattice of set partitions.

In this paper, we prove that there exists a maximal set of m directed Hamilton cycles in Dn if and only if n/2 m n − 1 for n 7. © 2007 Elsevier B.V. All rights reserved.

We correct the result of a previous paper which purported to show that L2(41) was not a subgroup of M. Our main result is that there is exactly one conjugacy class of subgroups L2(41) in the Monster. Such subgroups are self-normalizing and maximal. This leads to a new unexplained Moonshine phenomenon.

In a general social choice framework where the requirement of strategyproofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining....

In this study, sharp rearrangement inequalities for the fractional Bmaximal function Mα,γf are obtained in the Lorentz spaces Lp,q,γ and by using these inequalities the boundedness conditions of the operator Mα,γ are found. Then, the conditions for the boundedness of the Bmaximal operator Mγ are obtained in Lp,q,γ .