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Distances between factorizations in the Chicken McNugget monoid
Scott Chapman, Pedro Garcia-Sanchez, Christopher O'Neill
We use the Chicken McNugget monoid to demonstrate various factorization properties related to relations and chains of factorizations. We study in depth the catenary and tame degree…
When is a Puiseux monoid atomic?
Scott T. Chapman, Felix Gotti, Marly Gotti
A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If is a Puiseux monoid, then the question of whether each non-invertible element of can be wr…
Factorization invariants of Puiseux monoids generated by geometric sequences
Scott T. Chapman, Felix Gotti, Marly Gotti
We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerica…
So what is class number 2?
Scott T. Chapman
Using factorization properties, we give several characterizations for an algebraic number ring to have class number 2.
Beyond Coins, Stamps, and Chicken McNuggets: an Invitation to Numerical Semigroups
Scott Chapman, Rebecca Garcia, Christopher O'Neill
We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.