43 citations · 241 across the 35 of their papers we have counts for
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Systems of sets of lengths of Puiseux monoids
Felix Gotti
In this paper we study the system of sets of lengths of non-finitely generated atomic Puiseux monoids (a Puiseux monoid is an additive submonoid of ). We begin…
How do elements really factor in ?
Scott T. Chapman, Felix Gotti, Marly Gotti
Most undergraduate level abstract algebra texts use as an example of an integral domain which is not a unique factorization domain (or UFD) by exhibiting tw…
Puiseux monoids and transfer homomorphisms
Felix Gotti
There are several families of atomic monoids whose arithmetical invariants have received a great deal of attention during the last two decades. The factorization theory of finitely…
Positroids Induced by Rational Dyck Paths
Felix Gotti
A rational Dyck path of type is an increasing unit-step lattice path from to that never goes above the diagonal line . On the o…
The Chain Group of a Forest
Felix Gotti, Marly Gotti
For every labeled forest with set of vertices we can consider the subgroup of the symmetric group that is generated by all the cycles determined by all…
The Elasticity of Puiseux Monoids
Felix Gotti, Christopher O'Neill
Let be an atomic monoid and let be a non-unit element of . The elasticity of , denoted by , is the ratio of its largest factorization length to its shortest fac…
On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras
Felix Gotti, Marly Gotti
A molecule is a nonzero non-unit element of an integral domain (resp., commutative cancellative monoid) having a unique factorization into irreducibles (resp., atoms). Here we stud…
Minimal presentations of shifted numerical monoids
Rebecca Conaway, Felix Gotti, Jesse Horton +4
A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid , consider the family of "shifted" monoids obtained by adding to eac…
On three families of dense Puiseux monoids
Scott. T. Chapman, Felix Gotti, Marly Gotti +1
A positive monoid is a submonoid of the nonnegative cone of a linearly ordered abelian group. The positive monoids of rank are called Puiseux monoids, and their atomicity, arit…