The nematode Caenorhabditis elegans contains over 20 genes for TRP (transient receptor potential) channels which include members of all of the subclasses identified in mammalian cells. These proteins include three members of the TRPM (TRP melastatin) family: gon-2 (abnormal gonad development), gtl-1 (gon-2-like 1) and gtl-2. Although studies of these genes are at an early stage, we are beginnin...

2D-gon tilings with parallelograms are a model used in physics to study quasicrystals, and they are also important in combinatorics for the study of aperiodic structures. In this paper, we study the graph induced by the adjacency relation between tiles. This relation can been used to encode simply and efficiently 2D-gon tilings for algorithmic manipulation. We show for example how it can be use...

The Kepler-Bouwkamp constant is defined as the limit of radii of a sequence of concentric circles that are simultaneously inscribed in a regular n-gon and circumscribed around a regular (n + 1)-gon for n ≥ 3. The outermost circle, circumscribed around an equilateral triangle, has radius 1. We investigate what happens when the number of sides of regular polygons from the definition is given by a...

We compute the number of triangulations of a convex k-gon each of whose sides is subdivided by r−1 points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as k and/or r tend to infinity. We connect these results with the question of finding the planar set of points in general position that has the minimum possible number of triangul...

Let k be a field and let D be a k-linear algebraic triangulated category with split idempotents. Let Σ be the suspension functor of D and let s be a 2-spherical object of D, that is, the morphism space D(s,Σs) is k for i = 0 and i = 2 and vanishes otherwise. Assume that s classically generates D, that is, each object of D can be built from s using (de)suspensions, direct sums, direct summands, ...

A T E X-Tips ausgeholfen hat.

We show that an arrangement A of n lines in general position in the plane with n ≥ 3 has an inducing polygon of size n. The proof is constructive, that is we describe an algorithm that constructs a simple ngon inducing A.

Let n ≥ 3 be an integer. A convex lattice n-gon is a polygon whose n vertices are points on the integer lattice Z 2 and whose interior angles are strictly less than π. Let a n denote the least possible area enclosed by a convex lattice n-gon, then [1, 2, 3] {a n } ∞ n=3 = n 1 2

We study the planar central configurations of the 1 + n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2 ≤ n ≤ 4. Numerically, first we provide evidence that when n ≥ 9 the only central configuration is the regular n–gon with the large mass in its barycenter, and second we provide also evidence ...

Erdös asked whether every large enough set of points in general position in the plane contains six points that form a convex 6-gon without any points from the set in its interior. In this note we show how a set of 29 points was found that contains no empty convex 6-gon. To this end a fast incremental algorithm for finding such 6-gons was designed and implemented and a heuristic search approach ...