Advanced search
Publication Cover
The American Mathematical Monthly Volume 127, 2020 - Issue 8
Submit an article Journal homepage
406
Views
0
CrossRef citations to date
0
Altmetric
Notes

Elasticity in Apéry Sets

Jackson AutryTexas A&M University, Mailstop 3368, College Station, TX77843-3368
,
Tara GomesSan Diego State University, 5500 Campanile Dr., San Diego, CA92182-7720
,
Christopher O’NeillSan Diego State University, 5500 Campanile Dr., San Diego, CA92182-7720
&
Vadim PonomarenkoSan Diego State University, 5500 Campanile Dr., San Diego, CA92182-7720Correspondence[email protected]
Pages 744-749 | Received 16 Aug 2019, Accepted 20 Jan 2020, Published online: 21 Sep 2020

References

  • Alhajjar, E., Russell, T., Steward, M. (2019). Numerical semigroups and Kunz polytopes. Semigroup Forum. 99(1): 153–168. DOI: 10.1007/s00233-019-10028-x.
  • Apéry, R. (1946). Sur les branches superlinéaires des courbes algébriques. C. R. Acad. Sci. Paris. 222: 1198–1200.
  • Assi, A., García-Sánchez, P. A. (2016). Numerical Semigroups and Applications. RSME Springer Series, Vol. 1. Cham: Springer.
  • Baginski, P., Chapman, S. T. (2011). Factorizations of algebraic integers, block monoids, and additive number theory. Amer. Math. Monthly. 118(10): 901–920.
  • Barron, T., O’Neill, C., Pelayo, R. (2017). On the set of elasticities in numerical monoids. Semigroup Forum. 94(1): 37–50. DOI: 10.1007/s00233-015-9740-2.
  • Barucci, V., Dobbs, D., Fontana, M. (1997). Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains. Mem. Amer. Math. Soc. 125(598): x+78 pp.
  • Bras-Amorós, M. (2013). Numerical semigroups and codes. In: Moro, E. M., ed. Algebraic Geometry Modeling in Information Theory. Ser. Coding Theory Cryptol., Vol. 8. Hackensack, NJ: World Sci. Publ., pp. 167–218.
  • Chapman, S. T. (2019). So what is class number 2? Amer. Math. Monthly. 126(4): 330–339. DOI: 10.1080/00029890.2019.1562827.
  • Chapman, S. T., O’Neill, C. (2018). Factoring in the Chicken McNugget monoid. Math. Mag. 91(5): 323–336. DOI: 10.1080/0025570X.2018.1515559.
  • 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: 10.1016/j.ejc.2019.01.009.
  • Geroldinger, A., Halter-Koch, F. (2006). Non-unique Factorizations. Pure and Applied Mathematics, Vol. 278. Boca Raton, FL: Chapman & Hall/CRC.
  • Glenn, J., O’Neill, C., Ponomarenko, V., Sepanski, B. (2019). Augmented Hilbert series of numerical semigroups. Integers. 19: #A32.
  • Jenssen, M., Montealegre, D., Ponomarenko, V. (2013). Irreducible factorization lengths and the elasticity problem within N . Amer. Math. Monthly. 120(4): 322–328.
  • Kaplan, N. (2012). Counting numerical semigroups by genus and some cases of a question of Wilf. J. Pure Appl. Algebra. 216(5): 1016–1032.
  • Kaplan, N. (2017). Counting numerical semigroups. Amer. Math. Monthly. 124(9): 862–875.
  • Kiers, C., O’Neill, C., Ponomarenko, V. (2016). Numerical semigroups on compound sequences. Comm. Algebra. 44(9): 3842–3852.
  • Moree, P. (2014). Numerical semigroups, cyclotomic polynomials, and Bernoulli numbers. Amer. Math. Monthly. 121(10): 890–902.
  • O’Neill, C., Pelayo, R. (2015). How do you measure primality? Amer. Math. Monthly. 122(2): 121–137.
  • Pisinger, D., Toth, P. (1998). Knapsack problems. In: Du, D.-Z., Pardalos, P. M., eds. Handbook of Combinatorial Optimization, Vol. 1. Boston, MA: Kluwer Acad. Publ., pp. 299–428.
  • Rosales, J. C., García-Sánchez, P. A. (2009). Numerical Semigroups. Developments in Mathematics, Vol. 20. New York: Springer.
  • Wilf, H. S. (1978). A circle-of-lights algorithm for the “money-changing problem.” Amer. Math. Monthly. 85(7): 562–565.
  • Zhai, A. (2013). Fibonacci-like growth of numerical semigroups of a given genus. Semigroup Forum. 86(3): 634–662.
  • Zhao, Y. (2010). Constructing numerical semigroups of a given genus. Semigroup Forum. 80(2): 242–254.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.