2 citations · 3 across the 12 of their papers we have counts for
12 papers
Eventually nondecreasing quasi-polynomials
Benjamin Braun, Christopher O'Neill, Antwon Park
Quasi-polynomials are ubiquitous in combinatorics and algebra, as they arise in a variety of enumeration problems. Because quasi-polynomials consist of constituent polynomials, the…
Lengths of irreducible decompositions of numerical semigroups
Pedro Garcia-Sanchez, Christopher O'Neill
A numerical semigroup is an additive subsemigroup of the natural numbers that contains zero and has finite complement. A numerical semigroup is irreducible if it cannot be written…
Quasipolynomial behavior via constructibility in multigraded algebra
Hailong Dao, Ezra Miller, Jonathan Montaño +2
Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructib…
Numerical semigroups from rational matrices II: matricial dimension does not exceed multiplicity
Arsh Chhabra, Stephan Ramon Garcia, Christopher O'Neill
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least g…
Infinite free resolutions over numerical semigroup algebras via specialization
Tara Gomes, Christopher O'Neill, Aleksandra Sobieska +1
Each numerical semigroup with smallest positive element corresponds to an integer point in a polyhedral cone , known as the Kunz cone. The faces of form a strati…
Families of numerical semigroups and a special case of the Huneke-Wiegand conjecture
Miguel Landeros, Christopher O'Neill, Roberto Pelayo +3
The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical s…
Counting edges in factorization graphs of numerical semigroup elements
Mariah Moschetti, Christopher O'Neill
A numerical semigroup is an additively-closed set of non-negative integers, and a factorization of an element of is an expression of as a sum of generators of .…
Numerical semigroups, polyhedra, and posets IV: walking the faces of the Kunz cone
Cole Brower, Joseph McDonough, Christopher O'Neill
A numerical semigroup is a cofinite subset of containing and closed under addition. Each numerical semigroup with smallest positive element correspo…
The structure theorem for sets of length for numerical semigroups
Gilad Moskowitz, Christopher O'Neill
For sufficiently nice families of semigroups and monoids, the structure theorem for sets of length states that the length set of any sufficiently large element is an arithmetic seq…
Minimal free resolutions of numerical semigroup algebras via Apéry specialization
Benjamin Braun, Tara Gomes, Ezra Miller +2
Numerical semigroups with multiplicity are parameterized by integer points in a polyhedral cone , according to Kunz. For the toric ideal of any such semigroup, the main re…
On faces of the Kunz cone and the numerical semigroups within them
Levi Borevitz, Tara Gomes, Jiajie Ma +6
A numerical semigroup is a cofinite subset of the non-negative integers that is closed under addition and contains 0. Each numerical semigroup with fixed smallest positive elem…
On Atomic Density of Numerical Semigroup Algebras
A. A. Antoniou, R. A. C. Edmonds, B. Kubik +2
A numerical semigroup is a cofinite, additively-closed subset of the nonnegative integers that contains . In this paper, we initiate the study of atomic density, an asymptot…