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The
multidimensional Frobenius problem
Jeffrey Amos, Iuliana Pascu, Vadim Ponomarenko, Enrique Treviño and Yan Zhang |
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Vol. 4 (2011), No. 2, 187–197
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Abstract |
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We provide a variety of results concerning the problem of determining maximal vectors such that the Diophantine system has no solution: conditions for the existence of , conditions for the uniqueness of , bounds on , determining explicitly in several important special cases, constructions for , and a reduction for . |
Keywords
Frobenius, coin-exchange, linear Diophantine system
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Mathematical Subject Classification 2010
Primary: 11B75, 11D04, 11D72
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Milestones
Received: 2 March 2011
Revised: 9 May 2011
Accepted: 9 May 2011
Published: 17 January 2012
Communicated by Scott Chapman
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Authors |
| Jeffrey Amos | |
| Department of Mathematics Kansas State University Manhattan, KS 66506 United States |
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| Iuliana Pascu | |
| Department of Economics Massachusetts Institute of Technology 50 Memorial Drive Cambridge, MA 02142 United States |
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| Vadim Ponomarenko | |
| Department of Mathematics and
Statistics San Diego State University 5500 Campanile Drive San Diego CA 92182-7720 United States |
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| http://www-rohan.sdsu.edu/~vadim/ | |
| Enrique Treviño | |
| Department of Mathematics Dartmouth College Hanover, NH 03755 United States |
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| Yan Zhang | |
| Department of Mathematics Massachusetts Institute of Technology 50 Memorial Drive 77 Massachusetts Avenue Cambridge, MA 02139-4307 United States |
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| © 2011 MSP (Mathematical Sciences Publishers). |
