Skip to main content
14 events
when toggle format what by license comment
Jan 10, 2013 at 11:49 answer added Tim Seguine timeline score: 0
May 9, 2010 at 16:21 comment added SIB Thanks to you all for the discussion, answers, and references. It is really helpful.
S May 9, 2010 at 16:16 vote accept SIB
May 10, 2010 at 11:32
May 9, 2010 at 16:15 vote accept SIB
S May 9, 2010 at 16:16
May 9, 2010 at 15:27 answer added Torsten Ekedahl timeline score: 4
May 9, 2010 at 13:42 answer added Alexey Ustinov timeline score: 5
May 9, 2010 at 13:25 comment added Sidney Raffer Right: Thanks to Sergei Ivanov we can forget the "sufficiently large coordinate" idea. BUT -- The relevance of Ramirez-Alfonsin is that under some circumstances, we get a whole cone of representable b's.
May 9, 2010 at 9:44 comment added Pete L. Clark It seems to me that the theorem discussed in Section 6.5 of Ramirez-Alfonsin's book is not directly relevant to the question at hand. For instance, the matrix in Sergei Ivanonv's answer below satisfies the determinant condition (6.7) and thus admits a "pseudo-conductor". But this does not mean that every $b$ with sufficiently large coordinates is represented by non-negative integers.
May 9, 2010 at 9:03 comment added Wadim Zudilin @SJR: Thanks for the tip, I'll check whether it really covers the general matrix case, not only $k=1$ as in Pete Clark's solution below.
May 9, 2010 at 9:03 answer added Sergei Ivanov timeline score: 11
May 9, 2010 at 8:57 comment added Sidney Raffer There is a detailed discussion of your question in Section 6.5 of Alphonsin's book "The Diophantine Frobenius Problem"
May 9, 2010 at 8:50 history edited Pete L. Clark
added tags
May 9, 2010 at 8:11 comment added Wadim Zudilin I don't think that the problem is specially treated (some time ago I had a related one and nobody could suggest something concrete). You can write a general solution in the form $x_0+Ct$ where $x_0$ is a fixed solution and $Ct$ ($C$ a matrix and $t$ run over $\mathbb Z^l$) is a general solution of $Ax=0$. Then the required nonnegativity poses conditions on components $x_0+Ct$ (linear programming?). Since $x_0$ depends on $b$, you might be able to verify you expectation about large entries of $b$.
May 9, 2010 at 5:37 history asked SIB CC BY-SA 2.5