Effective Pila–Wilkie bounds for unrestricted Pfaffian surfaces

Bounds for Unrestricted Codes , by Linear Programming

The paper describes a problem of linear programming associated with distance properties of unrestricted codes. As a solution to the problem, one obtains an .upper bound for the number of words in codes having a prescribed set of distances. 1. Introduetion Important information about a code is contained in its Hamming distance distribution, defined as follows: for a q-ary code C of length n, it ...

Upper Bounds for Perfect Matchings in Pfaffian and Planar Graphs

We give upper bounds on weighted perfect matchings in Pfaffian graphs. These upper bounds are better than generalized Bregman’s inequality. We show that some of our upper bounds are sharp for 3 and 4-regular Pfaffian graphs. We apply our results to fullerene graphs.

Face-Width of Pfaffian Braces and Polyhex Graphs on Surfaces

A graph G with a perfect matching is Pfaffian if it admits an orientation D such that every central cycle C (i.e. C is of even size and G − V (C) has a perfect matching) has an odd number of edges oriented in either direction of the cycle. It is known that the number of perfect matchings of a Pfaffian graph can be computed in polynomial time. In this paper, we show that every embedding of a Pfa...

Enriques Surfaces and Other Non-pfaffian Subcanonical Subschemes of Codimension

Effective Bounds for Brauer Groups of Kummer Surfaces over Number Fields