In a recent paper, E. Steingŕımsson associated to each simple graph G a simplicial complex ∆G denoted as the coloring complex of G. Certain nonfaces of ∆G correspond in a natural manner to proper colorings of G. Indeed, the h-vector is an affine transformation of the chromatic polynomial χG of G, and the reduced Euler characteristic is, up to sign, equal to |χG(−1)| − 1. We show that ∆G is cons...

We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisfies McMullen’s g-theorem; in particular it is unimodal. This result generalizes a recent theorem of Athanasiadis (conjectured by Stanley) for compressed polytopes. It is derived from a more general theorem on Gorenstein affine normal monoids M: one can factor K[M] (K a field) by a “long” re...

Families of stable cyclic groups of nonlinear polynomial transformations of affine spaces K over general commutative ring K of increasing with n order can be used in the key exchange protocols and related to them El Gamal multivariate cryptosystems. We suggest to use high degree of noncommutativity of affine Cremona group and modify multivariate El Gamal algorithm via the usage of conjugations ...

We give a complete characterization of affine term structure models based on a general nonnegative Markov short rate process. This applies to the classical CIR model but includes as well short rate processes with jumps. We provide a link to the theory of branching processes and show how CBIprocesses naturally enter the field of term structure modelling. Using Markov semigroup theory we exploit ...

For multiparametric convex nonlinear programming problems we propose a recursive algorithm for approximating, within a given suboptimality tolerance, the value function and an optimizer as functions of the parameters. The approximate solution is expressed as a piecewise affine function over a simplicial partition of a subset of the feasible parameters, and it is organized over a tree structure ...

This paper describe the spaces spanned by the angle sums of certain classes of polytopes, as recorded in the α-vector. Families of polytopes are constructed whose angle sums span the spaces of polytopes defined by the Gram and Perles equations, analogs of the Euler and Dehn-Sommerville equations. This shows that the dimension of the affine span of the space of angle sums of simplices is ⌊ d−1 2...

We show that for all n ≥ 3 and all primes p there are infinitely many simplicial toric varieties of codimension n in the 2n-dimensional affine space whose minimum number of defining equations is equal to n in characteristic p, and lies between 2n − 2 and 2n in all other characteristics. In particular, these are new examples of varieties which are settheoretic complete intersections only in one ...