پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شماره‌ها | 1,673 |
| تعداد مقالات | 13,660 |
| تعداد مشاهده مقاله | 31,650,387 |
| تعداد دریافت فایل اصل مقاله | 12,501,625 |
On numerical semigroups with embedding dimension three | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 6، شماره 2، شهریور 2017، صفحه 1-6 اصل مقاله (219.27 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.20736 | ||
| نویسندگان | ||
| Ali Mahdavi؛ Farhad Rahmati* | ||
| Amirkabir University of Technology | ||
| چکیده | ||
| Let $f\neq1,3$ be a positive integer. We prove that there exists a numerical semigroup $S$ with embedding dimension three such that $f$ is the Frobenius number of $S$. We also show that the same fact holds for affine semigroups in higher dimensional monoids. | ||
| کلیدواژه‌ها | ||
| Frobenius number؛ Frobenius vector؛ Numerical semigroup؛ simplicial affine semigroup | ||
| مراجع | ||
|
[1] A. Assi, P. A. Garca-Sanchez and I. Ojeda, Frob enius vectors, Hilb ert series and Gluings of Affine Semigroups, J. Commut. Algebra , 7 (2015) 317{335.
[2] A. Assi, The Frob enius vector of a free affine semigroup, J. Algebra Appl., 11 (2012) 1-10.
[3] F. Curtis, On formulas for the Frob enius numb er of a numerical semigroup, Math. Scand, 67 (1990) 190-192.
[4] G. L. Feng and T. R. N. Rao, A simple approach for construction of algebraic-geometric co des from affine plane curves, IEEE Trans. Inform. Theory, 40 (1994) 1003-1012.
[5] R. Frob erg , The Frob enius numb er of some semigroups, Comm. Algebra, 22 (1994) 6021-6024.
[6] C. Kirfel and G. R. Pellikaan, The minimum distance of co des in an array coming from telescopic semigroups, (sp ecial issue), IEEE Trans. Inform. Theory, 41 (1995) 1720-1732.
[7] O. J. Rodseth, On a linear Diophantine problem of Frob enius, J. Reine Angew. Math., 301 (1978) 171-178.
[8] J. C. Rosales, P. A. Garca-Sanchez and J. I. Garcia-Garcia, Every p ositive integer is the Frob enius numb er of a numerical semigroup with three generators, Math. Scand., 94 (2004) 5-12.
[9] J. C. Rosales and P. A. Garca-Sanchez, Numerical Semigroups, Developments in mathematics, 20, Springer, New York, 2009.
[10] J. C. Rosales and P. A. Garca-Sanchez, On Cohen-Macaulay and gorenstein simplicial affine semigroups, Proc. Edinburgh Math. Soc. (2), 41 (1998) 517-537.
[11] J. C. Rosales and P. A. Garca-Sanchez, On free affine semigroups, Semigroup Forum, 58 (1999) 367-385.
[12] J. J. Sylvester, Mathematical questions with their solutions , Educational Times, 41 (1884) 171-178.
[13] B. Vizvari, Generation of uniformly distributed random vectors of good quality, Rutgers University, Rutgers Center for Op erations Research, 1994 1-11.
[14] B. Vizvari, On a generalization of the Frobenius problem, Technical Rep ort MN/30 Computer and Automation Inst., Hungarian Academy of Sciences, 1987. | ||
|
آمار تعداد مشاهده مقاله: 1,092 تعداد دریافت فایل اصل مقاله: 931 |
||