A realization theorem for sets of lengths in numerical monoids

References

[1] A. Assi and P. A. García-Sánchez, Numerical Semigroups and Applications, RSME Springer Ser. 1, Springer, Cham, 2016. 10.1007/978-3-319-41330-3Search in Google Scholar

[2] T. Barron, C. O’Neill and R. Pelayo, On the set of elasticities in numerical monoids, Semigroup Forum 94 (2017), no. 1, 37–50. 10.1007/s00233-015-9740-2Search in Google Scholar

[3] V. Barucci, Numerical semigroup algebras, Multiplicative Ideal Theory in Commutative Algebra, Springer, New York, (2006), 39–53. 10.1007/978-0-387-36717-0_3Search in Google Scholar

[4] V. Barucci, D. E. Dobbs and M. Fontana, Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Mem. Amer. Math. Soc. 125 (1997), no. 598, 1–78. 10.1090/memo/0598Search in Google Scholar

[5] C. Bowles, S. T. Chapman, N. Kaplan and D. Reiser, On delta sets of numerical monoids, J. Algebra Appl. 5 (2006), no. 5, 695–718. 10.1142/S0219498806001958Search in Google Scholar

[6] W. Bruns and J. Gubeladze, Polytopes, Rings, and K-Theory, Springer Monogr. Math., Springer, Dordrecht, 2009. 10.1007/b105283Search in Google Scholar

[7] S. T. Chapman, P. A. García-Sánchez and D. Llena, The catenary and tame degree of numerical monoids, Forum Math. 21 (2009), no. 1, 117–129. 10.1515/FORUM.2009.006Search in Google Scholar

[8] S. T. Chapman, R. Hoyer and N. Kaplan, Delta sets of numerical monoids are eventually periodic, Aequationes Math. 77 (2009), no. 3, 273–279. 10.1007/s00010-008-2948-4Search in Google Scholar

[9] S. Colton and N. Kaplan, The realization problem for delta sets of numerical semigroups, J. Commut. Algebra 9 (2017), no. 3, 313–339. 10.1216/JCA-2017-9-3-313Search in Google Scholar

[10] M. Delgado, P. A. García-Sánchez and J. Morais, “Numericalsgps”: A gap package on numerical semigroups, http://www.gap-system.org/Packages/numericalsgps.html. Search in Google Scholar

[11] S. Frisch, A construction of integer-valued polynomials with prescribed sets of lengths of factorizations, Monatsh. Math. 171 (2013), no. 3–4, 341–350. 10.1007/s00605-013-0508-zSearch in Google Scholar

[12] S. Frisch, S. Nakato and R. Rissner, Integer-valued polynomials on rings of algebraic integers of number fields with prescribed sets of lengths of factorizations, preprint (2017), https://arxiv.org/abs/1710.06783. Search in Google Scholar

[13] J. I. García-García, M. A. Moreno-Frías and A. Vigneron-Tenorio, Computation of delta sets of numerical monoids, Monatsh. Math. 178 (2015), no. 3, 457–472. 10.1007/s00605-015-0785-9Search in Google Scholar

[14] P. A. García-Sánchez, An overview of the computational aspects of nonunique factorization invariants, Multiplicative Ideal Theory and Factorization Theory, Springer Proc. Math. Stat. 170, Springer, Cham (2016), 159–181. 10.1007/978-3-319-38855-7_7Search in Google Scholar

[15] A. Geroldinger and F. Halter-Koch, Non-Unique Factorizations. Algebraic, Combinatorial and Analytic Theory, Pure Appl. Math. (Boca Raton) 278, Chapman & Hall/CRC, Boca Rato, 2006. 10.1201/9781420003208Search in Google Scholar

[16] A. Geroldinger, W. Hassler and G. Lettl, On the arithmetic of strongly primary monoids, Semigroup Forum 75 (2007), no. 3, 568–588. 10.1007/s00233-007-0721-ySearch in Google Scholar

[17] A. Geroldinger and W. A. Schmid, A realization theorem for sets of distances, J. Algebra 481 (2017), 188–198. 10.1016/j.jalgebra.2017.03.003Search in Google Scholar

[18] A. Geroldinger, W. A. Schmid and Q. Zhong, Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids, Rings, Polynomials, and Modules, Springer, Cham (2017), 191–235. 10.1007/978-3-319-65874-2_11Search in Google Scholar

[19] F. Gotti, On the atomic structure of Puiseux monoids, J. Algebra Appl. 16 (2017), no. 7, Article ID 1750126. 10.1142/S0219498817501262Search in Google Scholar

[20] F. Kainrath, Factorization in Krull monoids with infinite class group, Colloq. Math. 80 (1999), no. 1, 23–30. 10.4064/cm-80-1-23-30Search in Google Scholar

[21] C. O’Neill and R. Pelayo, Realizable sets of catenary degrees of numerical monoids, Bull. Aust. Math. Soc. (2017), 10.1017/S0004972717000995, https://arxiv.org/abs/1705.04276. 10.1017/S0004972717000995Search in Google Scholar

[22] M. Omidali, The catenary and tame degree of numerical monoids generated by generalized arithmetic sequences, Forum Math. 24 (2012), no. 3, 627–640. 10.1515/form.2011.078Search in Google Scholar

[23] W. A. Schmid, A realization theorem for sets of lengths, J. Number Theory 129 (2009), no. 5, 990–999. 10.1016/j.jnt.2008.10.019Search in Google Scholar