Delta sets for symmetric numerical semigroups with embedding dimension three

Abstract

This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three numerical semigroup. Also, as a consequence of these resutls, the sets that can be realized as Delta sets of numerical semigroups of embedding dimension three are fully characterized.2010 Mathematics Subject Classification. 05A17,20M13,20M14.

Which sets are sets of lengths in all numerical monoids?

“…The maximum of the set of distances is unknown (in terms of the atoms) and this question seems to have the same complexity as questions about the Frobenius number. For partial results and computational approaches we refer to [9,12,13,14].…”

Numerical semigroups with embedding dimension three and minimal catenary degree

“…In virtue of [11] and using the notation in Theorem 3.6, we have We distinguish five cases depending on the position of a in…”

Factoring in the Chicken McNugget Monoid

“…There is a wealth of recent work concerning the computation of the delta set of a numerical monoid [5,7,10,13,15,16,18,22]. For numerical monoids with three generators, the computation of the delta set is tightly related to Euclid's extended greatest common divisor algorithm [23,24]. We now summarize the main results in [ if r = 0, 6, 9, 15, where n = 20q + r for q, r ∈ N 0 and r < 20.…”