9 papers · 1 filter
Factorization length distribution for affine semigroups IV: a geometric approach to weighted factorization lengths in three-generator numerical semigroups
Stephan Ramon Garcia, Christopher O'Neill, Gabe Udell
For numerical semigroups with three generators, we study the asymptotic behavior of weighted factorization lengths, that is, linear functionals of the coefficients in the factoriza…
Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators
Stephan Ramon Garcia, Mohamed Omar, Christopher O'Neill +1
For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrar…
Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
Albrecht Boettcher, Stephan Ramon Garcia, Mohamed Omar +1
We employ the fact certain divided differences can be written as weighted means of B-splines and hence are positive. These divided differences include the complete homogeneous symm…
Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators
Stephan Ramon Garcia, Mohamed Omar, Christopher O'Neill +1
For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational r…
Wilf's conjecture in fixed multiplicity
Winfried Bruns, Pedro Garcia-Sanchez, Christopher O'Neill +1
We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity , and use it to prove Wilf's conjecture holds whenever $…
Sequentially embeddable graphs
Jackson Autry, Christopher O'Neill
We call a (not necessarily planar) embedding of a graph in the plane \emph{sequential} if its vertices lie in and the line segments between adjacent vertices cont…