The aim of the paper is to calculate face numbers of simple generalized permutohedra, and study their f -, hand γ-vectors. These polytopes include permutohedra, associahedra, graph-associahedra, simple graphic zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas for h-vectors and γ-vectors involving descent statistics. This includes a combinatorial interpret...

Abstract We consider a finite, connected and simple graph Γ that admits vertex-transitive group of automorphisms

The commuting graph of a group G, denoted by Γ(G), is a simple graph whose vertices are all non-central elements of G and two distinct vertices x, y are adjacent if xy = yx. In [1] it is conjectured that if M is a simple group and G is a group satisfying Γ(G) ∼= Γ(M), then G ∼= M . In this paper we prove this conjecture for many simple groups.

We begin the study of a tilting theory in certain truncated categories of modules G(Γ) for the current Lie algebra associated to a finite-dimensional complex simple Lie algebra, where Γ = P × J , J is an interval in Z, and P is the set of dominant integral weights of the simple Lie algebra. We use this to put a tilting theory on the category G(Γ′) where Γ′ = P ′×J , where P ′ ⊆ P is saturated. ...

X iv :0 90 7. 16 89 v1 [ m at h. C A ] 9 J ul 2 00 9 Small Gamma Products with Simple Values Albert Nijenhuis Introduction. Central as the gamma function is, it is surprising that its only known simple specific values are Γ(m) and Γ(m+ 1 2 ) for integral m. There are, however, numerous formulas that relate specific values of Γ to other functions, such as elliptic or hypergeometric functions or ...

0.1. Let Γ be a finite subgroup of SU(2). The question we will deal with in this paper is how an arbitrary (unitary) irreducible representation of SU(2) decomposes under the action of Γ. The theory of McKay assigns to Γ a complex simple Lie algebra g of type A−D−E. The assignment is such that if Γ̃ is the unitary dual of Γ we may parameterize Γ̃ by the nodes (or vertices) of the extended Coxeter-...

We consider systems of n parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations, and prove several convergence results in the limit n → ∞. The main aim of the paper is to study the convergence of the evolution...

In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness becomes small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel and Cassie equations for the a...

A 3D-2D dimensional reduction analysis for supremal functionals is performed in the realm of Γ-convergence. We show that the limit functional still admits a supremal representation, and we provide a precise identification of its density in some particular cases. Our results rely on an abstract representation theorem for the Γ-limit of a family of supremal functionals. Mathematics Subject Classi...

This paper deals with the passage from discrete to continuous in modeling the static elastic properties, in the setting of anti-planar linear elasticity, of vertical screw dislocations in a cylindrical crystal. We study, in the framework of Γ-convergence, the asymptotic behavior of the elastic stored energy induced by dislocations as the atomic scale ε tends to zero, in the regime of dilute dis...