The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences. (Q2890546)

A numerical monoid (called also numerical semigroup) is a subset \(S\) of positive integers closed under addition and containing all sufficiently large integers. The author gives explicit formulas for the catenary and tame degree of numerical monoids generated by sets of the form \(\{a,ha+d,ha+2d,\dots,ha+xd\}\), where \(a,d,h,x\) are positive integers and \((a,d)=1\). These formulas show that the difference between the tame degree and catenary degree can be arbitrary large, even if the number of generators is fixed.