8 papers
Bi-atomic classes of positive semirings
Nicholas R. Baeth, Scott T. Chapman, Felix Gotti
Let be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid and the multiplicative monoid $(S\s…
Length-factoriality in commutative monoids and integral domains
Scott T. Chapman, Jim Coykendall, Felix Gotti +1
An atomic monoid is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element no two distinct factorizations of have…
On length densities
Scott T. Chapman, Christopher O'Neill, Vadim Ponomarenko
For a commutative cancellative monoid , we introduce the notion of the length density of both a nonunit , denoted , and the entire monoid , denoted $\…
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…