We study some of the factorization invariants of the class of Puiseux monoids generated by
geometric sequences, and we compare and contrast them with the known results for …

A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If M is a
Puiseux monoid, then the question of whether each nonunit element of M can be written as a …

Let H be a commutative semigroup with unit element such that every non-unit can be written
as a finite product of irreducible elements (atoms). For every k∈ ℕ, let 𝒰 k (H) denote the set …

We examine the Delta set of a cancellative and reduced atomic monoid S where every set of
lengths of the factorizations of each element in S is bounded. In particular, we show the …

Let H be an atomic monoid. For x∈ H, let L (x) denote the set of all possible lengths of
factorizations of x into irreducibles. The system of sets of lengths of H is the set ℒ (H)={L (x) …

Every day, 34 million Chicken McNuggets are sold worldwide [4]. At most McDonalds
locations in the United States today, Chicken McNuggets are sold in packs of 4, 6, 10, 20 …

Abstract Let {a_1, ..., a_p\} a 1,…, ap be the minimal generating set of a numerical monoid S.
For any s ∈ S s∈ S, its Delta set is defined by Δ (s)={l_ i-l_ i-1 ∣ i= 2, ..., k\} Δ (s)= li-li-1∣ i …

Let H be a Krull monoid with infinite cyclic class group G and let GP⊂ G denote the set of
classes containing prime divisors. We study under which conditions on GP some of the main …

The delta set of a numerical semigroup S, denoted Δ(S), is a factorization invariant that
measures the complexity of the sets of lengths of elements in~ S. We study the following …

Let H be a Krull monoid with finite class group G such that every class contains a prime
divisor (for example, a ring of integers in an algebraic number field or a holomorphy ring in …