11 papers · 1 filter
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…
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 $\…
On parametrized families of numerical semigroups
Franklin Kerstetter, Christopher O'Neill
A numerical semigroup is an additive subsemigroup of the non-negative integers. In this paper, we consider parametrized families of numerical semigroups of the form $P_n = \langle…
Elasticity in Apery sets
Jackson Autry, Tara Gomes, Christopher O'Neill +1
A numerical semigroup is an additive subsemigroup of the non-negative integers, containing zero, with finite complement. Its multiplicity is its smallest nonzero element. T…
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.
Augmented Hilbert series of numerical semigroups
Jeske Glenn, Christopher O'Neill, Vadim Ponomarenko +1
A numerical semigroup is a subset of the non-negative integers containing that is closed under addition. The Hilbert series of (a formal power series equal to the sum o…