Bounds On Numerical Syzygies And Invariants

The BONSAI (Bounds On Numerical Syzygies And Invariants) project is aimed at investigating relations among generators and invariants of numerical semigroups and the rings associated to them, through theoretical and computational means. We consider a set of problems involving bounds for the Betti numbers of numerical semigroup rings, focusing on the first and last Betti numbers, which can be deduced from combinatorial data of the numerical semigroup.