Odd order Magic square with 0 Determinant
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From: AI on 1 Nov 2009 09:11 Can you find any Odd order Magic square with 0 Determinant or Prove that such Magic Square does not exist?
From: Gerry Myerson on 1 Nov 2009 21:25 In article <2f23e44b-1b92-4aa2-b503-072b285f38c1(a)h40g2000prf.googlegroups.com>, AI <vcpandya(a)gmail.com> wrote: > Can you find any Odd order Magic square with 0 Determinant or Prove > that such Magic Square does not exist? See Peter Loly, Ian Cameron, Walter Trump, Daniel Schindel, Magic square spectra, Linear Algebra and its Applications 430 (2009) 2659-2680. The abstract says, in part, Mattingly also proved that odd order regular magic squares have a zero eigenvalue with even multiplicity, m=0,2,4,... Analyzing results for natural fifth order magic squares from exact backtracking calculations we find 652 with m=2, and four with m=4. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Ken Pledger on 1 Nov 2009 22:09 In article <2f23e44b-1b92-4aa2-b503-072b285f38c1(a)h40g2000prf.googlegroups.com>, AI <vcpandya(a)gmail.com> wrote: > Can you find any Odd order Magic square with 0 Determinant or Prove > that such Magic Square does not exist? 13 14 11 15 22 1 10 2 26 Ken Pledger.
From: AI on 1 Nov 2009 22:50 Great!!! Thank you Ken Pledger for that magic square. I think odd order regular magic square from 1 to n with 0 determinant does not exist but others (such as you have given) exists. A Special Thanks to Gerry Myerson for interesting references.
From: Gerry Myerson on 2 Nov 2009 00:10
In article <ken.pledger-55F3B8.16094402112009(a)news.eternal-september.org>, Ken Pledger <ken.pledger(a)mcs.vuw.ac.nz> wrote: > In article > <2f23e44b-1b92-4aa2-b503-072b285f38c1(a)h40g2000prf.googlegroups.com>, > AI <vcpandya(a)gmail.com> wrote: > > > Can you find any Odd order Magic square with 0 Determinant or Prove > > that such Magic Square does not exist? > > > 13 14 11 > > 15 22 1 > > 10 2 26 That's what I'd call a semi-magic square - the rows and columns work, but not the diagonals. Also, I took OP to mean using the numbers 1, 2, ..., n^2, each exactly once. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email) |