English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We examine two natural operations to create numerical semigroups. We say thata numerical semigroup $\mathcal S$ is $k$-normalescent if it is the projectionof the set of integer points in a $k$-dimensional cone, and we say that$\mathcal S$ is a $k$-quotient if it is the quotient of a numerical semigroupwith $k$ generators. We prove that all $k$-quotients are $k$-normalescent, andalthough the converse is false in general, we prove that the projection of theset of integer points in a cone with $k$ extreme rays (possibly lying in adimension smaller than $k$) is a $k$-quotient. The discrete geometricperspective of studying cones is useful for studying $k$-quotients: inparticular, we use it to prove that the sum of a $k_1$-quotient and a$k_2$-quotient is a $(k_1+k_2)$-quotient. In addition, we prove several resultsabout when a numerical semigroup is not $k$-normalescent.

Numerical semigroups via projections and via quotients