A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Gröbner bases. Our main result is a bijection between virtual chambers of the configuration and virtual initial ideals of the associated binomial ideal.

We modify the Owen’s value of a TU game so as to consider the possibility that players organize themselves in coalitions that are not necessarily disjoint.

We present a quantitative method for selecting optimum configurations of computer systems. For each configuration we specify a set of requirements reflecting user’s needs. The level of satisfaction of requirements is called the global preference score. Using this indicator and the total cost of each configuration we solve the following optimization problems: (1) select a configuration which max...

An (nk)-configuration is a set of n points and n lines in the projective plane such that their point – line incidence graph is k-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. We provide an algorithm for generating, for given n and k, all topological (nk)-configurati...

A configuration (pq, nk) is a collection of p points and n straight lines in the Euclidean plane so that every point has q straight lines passing through it and every line has k points lying on it. A configuration is astral if it has precisely b q+1 2 c symmetry classes (transitivity classes) of lines and bk+1 2 c symmetry classes of points. An even astral configuration is an astral configurati...

We prove the existence of recurrent initial configurations for the rotor walk on many graphs, including Zd, and planar graphs with locally finite embeddings. We also prove that recurrence and transience of rotor walks are invariant under changes in the starting vertex and finite changes in the initial configuration.

Hatayama et al. conjectured fermionic formulas associated with tensor products of U ′ q (g)-crystals B. The crystals B correspond to the Kirillov–Reshetikhin modules which are certain finite dimensional U ′ q (g)-modules. In this paper we present a combinatorial description of the affine crystals Br,1 of type D n . A statistic preserving bijection between crystal paths for these crystals and ri...

We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound on the number of color sequences that can be realized from any such fixed point set and examine color sequences that can be realized regardless of the point...

A polar configuration is a triangle fan in a quad-dominant mesh; it allows for many mesh lines to join at a single polar vertex. This paper shows how a single tensor-product spline of degree (3, 6) can cap a polar configuration with a C surface. By design, this C polar spline joins C with surrounding bi-3 tensor-product splines and thereby complements algorithms that smoothly cap star-like, mul...

A d-dimensional ferromagnetic Ising model on a lattice torus is considered. As the size n of the lattice tends to infinity, the magnetic field a = a(n) and the pair potential depend on n. Precise bounds for the probability for local configurations to occur in a large ball are given. Under some conditions bearing on potentials a(n) and b(n), the distance between copies of different local configu...