8 papers
Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups
Theo Chinn, Junshu Feng, Stephan Ramon Garcia +1
We investigate matrices with entries in a number field such that some positive power has all its entries in the corresponding ring of integers. Our work generalizes previous result…
Rapidly growing AF algebras
Konrad Aguilar, Stephan Ramon Garcia, Evelyne Knight +2
We introduce certain families of AF algebras associated to Bratteli diagrams arising from numerical semigroup theory, a branch of combinatorics. Curry-Schoenberg B-splines, staples…
On -partial isometries: spectra, weighted shifts, and similarity
Mohamed Amine Aouichaoui, MichaÅ BuchaÅa, Stephan Ramon Garcia
The aim of this paper is to study -partial isometries on Hilbert spaces, a natural extension of partial isometries and -isometries. We establish structural and spectral resul…
Numerical semigroups from rational matrices IV: computation of the matricial dimensions of numerical semigroups with small Frobenius number or genus
Theo Chinn, Junshu Feng, Stephan Ramon Garcia +1
We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension…
Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture
Arsh Chhabra, Stephan Ramon Garcia
We characterize semigroups in of matricial dimension and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonel…
Factorization length distribution for affine semigroups V: explicit asymptotic behavior of weighted factorization lengths on numerical semigroups
Stephan Ramon Garcia, Gabe Udell
We describe the asymptotic behavior of weighted factorization lengths on numerical semigroups. Our approach is geometric as opposed to analytic, explains the presence of Curry-Scho…