Advanced search
Publication Cover
Communications in Algebra Volume 37, 2009 - Issue 2
Submit an article Journal homepage
120
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On the Frobenius Problem of Numerical Semigroups

Eli Leher School of Mathematics, Tel-Aviv University, Tel-Aviv, IsraelCorrespondence[email protected] ; [email protected]
Pages 639-649 | Received 27 Apr 2007, Published online: 09 Feb 2009

REFERENCES

  • Apéry , R. ( 1946 ). Sur les branches superlinéaires des courbes algébriques . C. R. Acad. Sci. Paris 222 : 1198 – 1200 .
  • Brauer , A. ( 1942 ). On a problem of partitions . Amer. J. Math. 64 : 299 – 312 .
  • Brauer , A. , Seelbinder , B. M. ( 1954 ). On a problem of partitions II . Amer. J. Math. 76 : 343 – 346 .
  • Brauer , A. , Shockley , J. E. ( 1962 ). On a problem of Frobenius . J. Reine Angew. Math. 211 : 215 – 220 .
  • Delorme , C. ( 1976 ). Sous-monoïdes d'intersection complètes de N . Ann. Sci. Éc. Norm. Sup. 4 Serie, T. 9 , 145 – 154 .
  • Denham , G. ( 2003 ). Short generating functions for some semigroup algebras . Elec. J. Combinatorics 10 .
  • Estrada , M. , López , A. ( 1994 ). A note on symmetric semigroups and almost arithmetic sequences . Commun. Alg. 22 ( 10 ): 3903 – 3905 .
  • Fröberg , R. ( 1994 ). The Frobenius number of some semigroups . Commun. Alg. 22 : 6021 – 6024 .
  • Herzog , J. ( 1970 ). Generators and relations of abelian semigroups and abelian semigroup rings . Manuscripta Math. 3 : 175 – 193 .
  • Juan , L. ( 1993 ). Some results about symmetric semigroups . Commun. Alg. 21 ( 10 ): 3637 – 3645 .
  • Leher , E. ( 2007 ). Applications of the Minimal Transversal Method in Numerical Semigroups. Ph.D. thesis. Tel Aviv Univ., Tel Aviv, Israel .
  • Leher , E. ( 2008 ). Bounds for the genus of a numerical semigroups . Inter. J. Number Theory 4 ( 5 ): 827 – 834 .
  • Leher , E. , Rosset , S. A note on the Hilbert series of complete intersections numerical semigroups . Submitted .
  • Nijenhuis , M. , Wilf , H. S. ( 1972 ). Representations of integers by linear forms in nonnegative integers . J. Number Theory 4 : 98 – 106 .
  • Ramirez Alfonsin , J. L. (2005). The Diophantine Frobenius Problem . Oxford Lecture Series in Mathematics and Its Applications 30. Oxford Press, pp. 486–487.
  • Roberts , J. B. ( 1956 ). Note on linear forms . Proc. Amer. Math. Soc. 7 : 465 – 469 .
  • Selmer , E. S. ( 1977 ). On the linear diophantine problem of Frobenius . J. Für Reine Und Angewandte Mathematik 293/294 ( 1 ): 1 – 17 .
  • Sylvester , J. J. ( 1884 ). Problem 7382 . Educational Times 37 : 26 .
  • Sylvester , J. J. , Curran Sharp , W. J. ( 1884 ). Problem 7382 . Educational Times 41 : 171 – 178 .
  • Communicated by A. K. Singh.

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.