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 …

Nonunique factorization in commutative monoids is often studied using factorization
invariants, which assign to each monoid element a quantity determined by the factorization …

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the
non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants …

Let H be an atomic monoid (eg, the multiplicative monoid of a noetherian domain). For an
element b∈ H, let ω (H, b) be the smallest N∈ N0∪{∞} having the following property: if n∈ …

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 …

Studying the factorization theory of numerical monoids relies on understanding several
important factorization invariants, including length sets, delta sets, and $\omega $-primality …

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 …

Studying certain combinatorial properties of non-unique factorizations have been a subject
of recent literature. Little is known about two combinatorial invariants, namely the catenary …

We give an algorithm to compute the ω-primality of finitely generated atomic monoids.
Asymptotic ω-primality is also studied and a formula to obtain it in finitely generated quasi …

In commutative monoids, the ω-value measures how far an element is from being prime.
This invariant, which is important in understanding the factorization theory of monoids, has …