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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…
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…
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…