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Length density and numerical semigroups
Cole Brower, Scott Chapman, Travis Kulhanek +4
Length density is a recently introduced factorization invariant, assigned to each element of a cancellative commutative atomic semigroup , that measures how far the set of f…
Atomicity of Positive Monoids
Scott T. Chapman, Marly Gotti
An additive submonoid of the nonnegative cone of the real line is called a positive monoid. Positive monoids consisting of rational numbers (also known as Puiseux monoids) have bee…
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…