Lunedì 14 Ottobre 2019 alle ore 14:30
Sala Conferenze "F. Tricerri" Dipartimento di Matematica e Informatica "U. Dini"
"Coordinatizing n_3 Configurations"
Prof. William Kocay
St. Paul's College
University of Manitoba
An n_3 configuration consists of n points and n lines such that every
point is on 3 lines and every line contains 3 points. For example,
the Fano configuration is a 7_3 configuration.
Given an n_3 configuration, a one-point extension is a technique that constructs
(n+1)_3 configurations from it. A configuration is geometric if it
can be realized by a collection of points and straight lines in the plane.
Given a geometric n_3 configuration with a planar coordinatization of its
points and lines, a method is presented that uses a one-point extension to
produce (n+1)_3 configurations from it, and then constructs geometric realizations of
the (n+1)_3 configurations. It is shown that this can be done using only a homogeneous
cubic polynomial in just three variables, independent of n.
This transforms a computationally intractable
problem into a computationally practical one.