| Title:
|
On the Frobenius number of a modular Diophantine inequality (English) |
| Author:
|
Rosales, J. C. |
| Author:
|
Vasco, P. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
367-375 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an algorithm for computing the greatest integer that is not a solution of the modular Diophantine inequality $ax \mod b\leq x$, with complexity similar to the complexity of the Euclid algorithm for computing the greatest common divisor of two integers. (English) |
| Keyword:
|
numerical semigroup |
| Keyword:
|
Diophantine inequality |
| Keyword:
|
Frobenius number |
| Keyword:
|
multiplicity |
| MSC:
|
11D75 |
| MSC:
|
20M14 |
| idZBL:
|
Zbl 1174.11046 |
| idMR:
|
MR2472485 |
| DOI:
|
10.21136/MB.2008.140626 |
| . |
| Date available:
|
2010-07-20T17:37:48Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140626 |
| . |
| Reference:
|
[1] Barucci, V., Dobbs, D. E., Fontana, M.: Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains.Memoirs of the Amer. Math. Soc. 598 (1997). Zbl 0868.13003, MR 1357822 |
| Reference:
|
[2] Delgado, M., Rosales, J. C.: On the Frobenius number of a proportionally modular Diophantine inequality.Portugaliae Mathematica 63 (2006), 415-425. Zbl 1172.11011, MR 2287275 |
| Reference:
|
[3] Alfonsín, J. L. Ramírez: The Diophantine Frobenius Problem.Oxford Univ. Press (2005). MR 2260521 |
| Reference:
|
[4] Rosales, J. C.: Modular Diophantine inequalities and some of their invariants.Indian J. Pure App. Math. 36 (2005), 417-429. Zbl 1094.20037, MR 2199217 |
| Reference:
|
[5] Rosales, J. C., García-Sánchez, P. A.: Finitely Generated Commutative Monoids.Nova Science Publishers, New York (1999). MR 1694173 |
| Reference:
|
[6] Rosales, J. C., García-Sánchez, P. A., a-García, J. I. Garcí, Urbano-Blanco, J. M.: Proportionally modular Diophantine inequalities.J. Number Theory 103 (2003), 281-294. MR 2020273, 10.1016/j.jnt.2003.06.002 |
| Reference:
|
[7] Rosales, J. C., García-Sánchez, P. A., Urbano-Blanco, J. M.: Modular Diophantine inequalities and numerical semigroups.Pacific J. Math. 218 (2005), 379-398. Zbl 1184.20052, MR 2218353, 10.2140/pjm.2005.218.379 |
| Reference:
|
[8] Rosales, J. C., Urbano-Blanco, J. M.: Opened modular numerical semigroups.J. Algebra 306 (2006), 368-377. Zbl 1109.20052, MR 2271340, 10.1016/j.jalgebra.2006.08.009 |
| Reference:
|
[9] Rosales, J. C., Vasco, P.: The smallest positive integer that is solution of a proportionally modular Diophantine inequality.Math. Inequal. Appl. 11 (2008), 203-212. Zbl 1142.20042, MR 2410272 |
| . |
