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, graphical zonotopes, nestohedra, and other interesting polytopes. We give several explicit formulas involving descent statistics, calculate generating functions and discuss their relationship with Simon...

Let the braid group Bn act as (isotopy classes of) diffeomorphisms of an n-punctured disc Dn. Then there is an action of Bn on a polynomial algebra R = C [a1 , . . . , aN ] and a way of representing simple closed curves on Dn as elements of R. Fix k ∈ 2N. Using this approach we show that the image in Aut(R) of each Dehn twist τ about a simple closed γ in Dn satisfies a kind of characteristic eq...

This paper describes a tool called Explain for performing abductive inference. Logical abduction is the problem of finding a simple explanatory hypothesis that explains observed facts. Specifically, given a set of premises Γ and a desired conclusion φ, abductive inference finds a simple explanation ψ such that Γ ∧ ψ |= φ, and ψ is consistent with known premises Γ . Abduction has many useful app...

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) ≥ 2 and let Γ be a uniform lattice in G. (a) If CH holds, then Γ has a unique asymptotic cone up to homeomorphism. (b) If CH fails, then Γ has 2 ω asymptotic cones up to homeomorphism.

Asymmetric and site-selective formal [3 + 2]-annulations of γ-alkyl-β,γ-unsaturated γ-lactams with α,β-unsaturated aldehydes have been developed. These organocatalysed transformations yield high value enantioenriched bicyclic γ-lactams with up to four new stereocenters (sometimes including a quarternary carbon). The overall transformation starts from simple and readily accessible furans and ove...

This note describes a unified approach to several superrigidity results, old and new, concerning representations of lattices into simple algebraic groups over local fields. For an arbitrary group Γ and a boundary action Γ y B we associate certain generalized Weyl group WΓ,B and show that any representation with a Zariski dense unbounded image in a simple algebraic group, ρ : Γ → H, defines a sp...

Let Γ be a simple graph and I ( x ) its multivariate independence polynomial. The main result of this paper is the characterization chordal graphs as only for which power series expansion − 1 Horn hypergeometric.

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L2(49). As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L2(49) except L2(49) · 22. Also, we prove that if M is an almost simple group relate...

Let ∆ be an infinite, locally finite tree with more than two ends. Let Γ < Aut(∆) be an acylindrical uniform lattice. Then the boundary algebra AΓ = C(∂∆) Γ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.

We prove that any real-analytic, volume-preserving action of a lattice Γ in a simple Lie group with Q-rank(Γ) ≥ 7 on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.