The Frobenius problem for Mersenne numerical semigroups
Tóm tắt
In this paper, we give formulas for the embedding dimension, the Frobenius number, the type and the genus for a numerical semigroups generated by the Mersenne numbers greater than or equal to a given Mersenne number.
Tài liệu tham khảo
Apéry, R.: Sur les branches superlinéaires des courbes algébriques. C. R. Acad. Sci. Paris 222, 1198–1200 (1946)
Ramirez Alfonsín, J.L.: The Diophantine Frobenius Problem. Oxford University Press, London (2005)
Rosales, J.C., Branco, M.B.: Numerical semigroups that can be expressed as an intersection of symmetric numerical semigroups. J. Pure Appl. Algebra 171, 303–314 (2002)
Rosales, J.C., García-Sánchez, P.A.: Numerical semigroups, Developments in Mathematics, vol. 20. Springer, New York (2009)
Selmer, E.S.: On linear diophantine problem of Frobenius. J. Reine Angew. Math. 293(294), 1–17 (1977)
Sylvester, J.J.: On subvariants, i.e. Semi-invariants to binary quantics of an unlimited order. Am. J. Math. 5, 79–136 (1882)
Sylvester, J.J.: Problem 7382, The educational Times, and Journal of College Of Preceptors, New Series, 36 (266) (1883), 177. Solution by W.J. Curran Sharp, ibid. 36 (271) (1883). Republished as [9]
Sylvester, J.J.: Mathematical Questions with Their Solutions, Educational Times, vol. 41. Francis Hodson, London (1884)