Craig Larson, Virginia Commonwealth University

Abstract

I will describe the ideas underlying the program CONJECTURING which can be used to make conjectures about upper or lower bounds of invariants (or necessary or sufficient conditions for properties) for a wide variety of mathematical objects. The conjecturing heuristic is the heuristic Fajtlowicz used in his Graffiti program; our program has been broadly generalized to be useful in many domains - and the code is open source, and can be installed as a Sage package. We will give several examples of theorems conjectured by the program, as well as a selection of open conjectures. We will also mention ways to leverage the program to maximize its utility as a tool for researchers. This is joint work with Nico Van Cleemput (Ghent University)