8 papers
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…
Curriculum Guidelines for Undergraduate Programs in Data Science
Richard De Veaux, Mahesh Agarwal, Maia Averett +22
The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group cons…
Apéry sets of shifted numerical monoids
Christopher O'Neill, Roberto Pelayo
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
Realizable sets of catenary degrees of numerical monoids
Christopher O'Neill, Roberto Pelayo
The catenary degree is an invariant that measures the distance between factorizations of elements within an atomic monoid. In this paper, we classify which finite subsets of $\math…
Minimal presentations of shifted numerical monoids
Rebecca Conaway, Felix Gotti, Jesse Horton +4
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
On Delta Sets and their Realizable Subsets in Krull Monoids with Cyclic Class Groups
Scott T. Chapman, Felix Gotti, Roberto Pelayo
Let be a commutative cancellative monoid. The set , which consists of all positive integers which are distances between consecutive factorization lengths of elements in $…