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

Recent investigations on the catenary degrees of numerical monoids havedemonstrated that this invariant is a powerful tool in understanding thefactorization theory of this class of monoids. Although useful, the catenarydegree is largely not sensitive to the lengths of factorizations of an element.In this paper, we study the monotone catenary degree of numerical monoids,which is a variant of catenary degree that requires chains run throughfactorization lengths monotonically. In general, the monotone catenary isgreater than or equal to the catenary degree. We begin by providing animportant class of monoids (arithmetical numerical monoids) for which monotonecatenary degree is equal to the catenary degree. Conversely, we provide severalclasses of embedding dimension 3 numerical monoids where monotone catenarydegree is strictly greater. We conclude by showing that this difference cangrow arbitrarily large.

Monotone Catenary Degree in Numerical Monoids