For a positive integer n that is not a power of 2, precisely the same family of convex polygons with n sides is optimal in three different geometric problems. These polygons have maximal perimeter relative to their diameter, maximal width relative to their diameter, and maximal width relative to their perimeter. We study the number of different convex n-gons E(n) that are extremal in these thre...

The distribution of viruses inhabiting the coral mucus remains undetermined, as there is no suitable standardized procedure for their separation from this organic matrix, principally owing to its viscosity and autofluorescence. Seven protocols were tested, and the most efficient separations were obtained from a chemical treatment requiring potassium citrate.

We present an algorithm for enumerating without repetitions all the planar (noncrossing) minimally rigid (Laman) graphs embedded on a given generic set of n points. Our algorithm is based on the Reverse search paradigm of Avis and Fukuda. It generates each output graph in O(n) time and O(n) space, or, with a slightly different implementation, in O(n) time and O(n) space. In particular, we obtai...

By means of the Cayley Trick the problem of enumerating all regular ne mixed subdivisions is reduced to enumerating all regular triangulations. The set of all regular triangulations is well-understood thanks to the bijection with the vertices of the secondary polytope. However, since we are only interested in the conngurations of mixed cells in a mixed subdivision, we want to avoid dealing with...

We study the complexity of the problem of enumerating all graphs with frequency at least 1 and computing their support.