ar X iv : m at h / 07 02 50 9 v 1 [ m at h . C O ] 1 7 Fe b 20 07 A half - space approach to order dimension Stephan Foldes and

ar X iv : m at h / 07 02 50 9 v 1 [ m at h . C O ] 1 7 Fe b 20 07 A half - space approach to order dimension

The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.

ar X iv : m at h / 06 02 37 1 v 1 [ m at h . A G ] 1 7 Fe b 20 06 Braid Monodromy of Hypersurface Singularities

ar X iv : m at h / 02 02 11 4 v 1 [ m at h . G N ] 1 2 Fe b 20 02 ON FINITE - DIMENSIONAL MAPS II

Let f : X → Y be a perfect n-dimensional surjective map of paracompact spaces and Y a C-space. We consider the following property of continuous maps g : X → Ik = [0, 1], where 1 ≤ k ≤ ω: each g(f(y)), y ∈ Y , is at most n-dimensional. It is shown that all maps g ∈ C(X, In+1) with the above property form a dense Gδ-set in the function space C(X, I n+1 ) equipped with the source limitation topolo...

ar X iv : m at h / 03 02 20 2 v 1 [ m at h . C O ] 1 8 Fe b 20 03 PERIODIC DE BRUIJN TRIANGLES : EXACT AND ASYMPTOTIC RESULTS

We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution. §

ar X iv : m at h / 03 02 33 9 v 1 [ m at h . A P ] 2 7 Fe b 20 03 NONLINEAR SCHRÖDINGER EQUATIONS WITH STARK POTENTIAL

We study the nonlinear Schrödinger equations with a linear potential. A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential.