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1. Factorization length distribution for affine semigroups I: Numerical semigroups with three generators

   https://doi.org/10.1016/j.ejc.2019.01.009  

   Garcia, Stephan Ramon; O’Neill, Christopher; Yih, Samuel (May 2019, European Journal of Combinatorics)
2. Malcolmson semigroups

   https://doi.org/10.1016/j.jalgebra.2023.01.031  

   Hung, Tsz Fun; Li, Hanfeng (June 2023, Journal of Algebra)
3. Holonomy theorem for finite semigroups

   https://doi.org/10.1142/S0218196722500217  

   Rhodes, John; Schilling, Anne; Silva, Pedro V. (May 2022, International Journal of Algebra and Computation)

   In this paper, we provide a simple proof of the Holonomy theorem using a new Lyndon–Chiswell length function on the Karnofsky–Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps. 

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4. FACTORIZATION LENGTH DISTRIBUTION FOR AFFINE SEMIGROUPS III: MODULAR EQUIDISTRIBUTION FOR NUMERICAL SEMIGROUPS WITH ARBITRARILY MANY GENERATORS

   https://doi.org/10.1017/S1446788720000476  

   GARCIA, STEPHAN RAMON; OMAR, MOHAMED; O’NEILL, CHRISTOPHER; WESLEY, TIMOTHY (August 2022, Journal of the Australian Mathematical Society)

   Abstract For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization lengths are equidistributed across all congruence classes that are not trivially ruled out by modular considerations. 

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5. Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups

   https://doi.org/10.1515/advgeom-2021-0024  

   Autry, Jackson; Ezell, Abigail; Gomes, Tara; O’Neill, Christopher; Preuss, Christopher; Saluja, Tarang; Davila, Eduardo Torres (January 2022, Advances in Geometry)

   Abstract Several recent papers have examined a rational polyhedronP_mwhose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containingm. A combinatorial description of the faces ofP_mwas recently introduced, one that can be obtained from the divisibility posets of the numerical semigroups a given face contains. In this paper, we study the faces ofP_mcontaining arithmetical numerical semigroups and those containing certain glued numerical semigroups, as an initial step towards better understanding the full face structure ofP_m. In most cases, such faces only contain semigroups from these families, yielding a tight connection to the geometry ofP_m. 

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