The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences

TL;DR

This paper investigates the catenary and tame degrees of numerical monoids generated by generalized arithmetic sequences, providing explicit computations and revealing that their difference can be arbitrarily large.

Contribution

It computes the catenary and tame degrees for a specific class of numerical monoids and demonstrates that their difference can be unbounded even with a fixed number of generators.

Findings

Computed catenary and tame degrees for generalized arithmetic sequence monoids

Showed the difference between degrees can be arbitrarily large

Provided new insights into factorization invariants of numerical monoids

Abstract

Studying ceratin combinatorial properties of non-unique factorizations have been a subject of recent literatures. Little is known about two combinatorial invariants, namely the catenary degree and the tame degree, even in the case of numerical monoids. In this paper we compute these invariants for a certain class of numerical monoids generated by generalized arithmetic sequences. We also show that the difference between the tame degree and the catenary degree can be arbitrary large even if the number of minimal generators is fixed.