References
- Abhyankar, S. S. (1967). Local rings of high embedding dimension. Amer. J. Math. 89(4):1073–1077. DOI: https://doi.org/10.2307/2373418.
- Amos, J., Chapman, S. T., Hine, N., Paixão, J. (2007). Sets of lengths do not characterize numerical monoids. Integers 7(1):A50.
- Baeth, N. R., Smertnig, D. (2015). Factorization theory: from commutative to noncommutative settings. J. Algebra 441:475–551. DOI: https://doi.org/10.1016/j.jalgebra.2015.06.007.
- Baeth, N. R., Wiegand, R. (2013). Factorization theory and decompositions of modules. Amer. Math. Monthly 120(1):3–34.
- Baginski, P., Chapman, S. T. (2011). Factorizations of algebraic integers, block monoids, and additive number theory. Amer. Math. Monthly 118(10):901–920. DOI: https://doi.org/10.4169/amer.math.monthly.118.10.901.
- Banister, M., Chaika, J., Chapman, S.T., Meyerson, W. (2007). On the arithmetic of arithmetical congruence monoids. Colloq. Math. 108(1):105–118. DOI: https://doi.org/10.4064/cm108-1-9.
- Barron, T., O’Neill, C., Pelayo, R. (2017). On the set of elasticities in numerical monoids. Semigroup Forum 94(1):37–50. DOI: https://doi.org/10.1007/s00233-015-9740-2.
- Barucci, V., Dobbs, D. E., Fontana, M. (1997). Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains, Vol. 598. Providence, RI: American Mathematical Society.
- Billingsley, P. (2012). Probability and Measure. Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons, Inc. Anniversary edition [of MR1324786], With a foreword by Steve Lalley and a brief biography of Billingsley by Steve Koppes.
- Bryant, L., Hamblin, J. (2013). The maximal denumerant of a numerical semigroup. Semigroup Forum 86:571–582. DOI: https://doi.org/10.1007/s00233-012-9448-5.
- Cahen, P.-J., Chabert, J.-L. (1997). Integer-Valued Polynomials. Mathematical Surveys and Monographs, Vol. 48. Providence, RI: American Mathematical Society.
- Chapman, S. T., Coykendall, J. (2000). Half-factorial domains, a survey. In: Chapman, S. T., Glaz, S., eds. Non-Noetherian Commutative Ring Theory. Boston, MA: Springer, pp. 97–115.
- Chapman, S. T., Gotti, F., Pelayo, R. (2014). On delta sets and their realizable subsets in Krull monoids with cyclic class groups. Colloq. Math. 137(1):137–146. DOI: https://doi.org/10.4064/cm137-1-10.
- Gao, W., Geroldinger, A. (2000). Systems of sets of lengths II. Abh. Math. Sem. Univ. Hamburg 70:31–49. DOI: https://doi.org/10.1007/BF02940900.
- Garcia, S. R., Omar, M., O'Neill, C., Wesley, S. (2021). Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators. J. Austral. Math. Soc. in press. DOI: https://doi.org/10.1017/S1446788720000476.
- Garcia, S. R., Omar, M., O'Neill, C., Yih, S. (2021). Factorization length distribution for affine semigroups II: asymptotic behavior for numerical semigroups with arbitrarily many generators. J. Combin. Theory Ser. A 178:105358–105334. DOI: https://doi.org/10.1016/j.jcta.2020.105358.
- Garcia, S. R., O'Neill, C., Yih, S. (2019). Factorization length distribution for affine semigroups I: numerical semigroups with three generators. European J. Combin. 78:190–204. DOI: https://doi.org/10.1016/j.ejc.2019.01.009.
- García Sánchez, P. A., Ojeda, I., Rosales, J. C. (2013). Affine semigroups having a unique Betti element. J. Algebra Appl. 12(3):1250177. DOI: https://doi.org/10.1142/S0219498812501770.
- Geroldinger, A. (1998). A structure theorem for sets of lengths. Colloq. Math. 78(2):225–259. DOI: https://doi.org/10.4064/cm-78-2-225-259.
- Geroldinger, A. (2016). Sets of lengths. Amer. Math. Monthly 123(10):960–988.
- Geroldinger, A., Halter-Koch, F. (1992). On the asymptotic behaviour of lengths of factorizations. J. Pure Appl. Algebra 77(3):239–252. DOI: https://doi.org/10.1016/0022-4049(92)90140-B.
- Geroldinger, A., Halter-Koch, F. (2006). Non-unique Factorizations: Algebraic, Combinatorial and Analytic Theory. Pure and Applied Mathematics, Vol. 278. Boca Raton, FL: Chapman & Hall/CRC.
- Geroldinger, A., Halter-Koch, F. (2006). Non-unique factorizations: a survey. In: Brewer, J. W., Glaz, S., Heinzer, W. J., Olberding, B. M., eds. Multiplicative Ideal Theory in Commutative Algebra. Boston, MA: Springer, pp. 207–226.
- Geroldinger, A., Schmid, W. A. (2018). A realization theorem for sets of lengths in numerical monoids. Forum Math. 30(5):1111–1118. DOI: https://doi.org/10.1515/forum-2017-0180.
- Kerstetter, F., O'Neill, C. (2020). On parametrized families of numerical semigroups. Commun. Algebra 48(11):4698–4717. DOI: https://doi.org/10.1080/00927872.2020.1769122.
- Narkiewicz, W. (1979). Finite abelian groups and factorization problems. Colloq. Math. 42(1):319–330. DOI: https://doi.org/10.4064/cm-42-1-319-330.
- O'Neill, C. (2017). On factorization invariants and Hilbert functions. J. Pure Appl. Algebra 221(12):3069–3088.
- O'Neill, C., Pelayo, R. (2017). Factorization invariants in numerical monoids. In: Harrington, H. A., Omar, M., Wright, M., eds. Algebraic and Geometric Methods in Discrete Mathematics. Contemporary Mathematics, Vol. 685. Providence, RI: American Mathematical Society, pp. 231–249.
- Rosales, J. C., García-Sánchez, P. A. (2009). Numerical Semigroups. Developments in Mathematics, Vol. 20. New York: Springer.
- Schmid, W. A. (2009). Characterization of class groups of Krull monoids via their systems of sets of lengths: a status report. In: Adhikari, S. D., Ramakrishnan, B., eds. Number Theory and Applications. Gurgaon: Hindustan Book Agency, pp. 189–212.