Timeline for Circulant matrix with integer entries and determinant 1 or -1
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 29, 2014 at 10:29 | comment | added | Fabienne | Thanks a lot for all your answers. I was convinced it was true. Is there a name for a matrix like a circulant but where the i-th column is a permutation f_i of the first column and f_i not necessarily (1,2, ..,n)^i? | |
| May 27, 2014 at 23:39 | comment | added | Gerry Myerson | Regarding the "Experimentally" edit, for even $n$ the determinant is the product of $(1+w^3)/(1+w)$ taken over all solutions $w$ of $w^{n+3}=1$. If $\gcd(n,3)=1$, then the numerator and denominator run over the same numbers, so this product is 1. | |
| May 27, 2014 at 13:52 | history | edited | joro | CC BY-SA 3.0 |
Bigger c_i
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| May 27, 2014 at 12:49 | comment | added | Jeremy Rickard | There's a paper "Unimodular Integer Circulants" by John Cremona that studies this question in some depth: homepages.warwick.ac.uk/~masgaj/papers/unicirculant.pdf | |
| May 27, 2014 at 12:00 | history | edited | joro | CC BY-SA 3.0 |
Added more counterexample and OEIS reference
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| May 27, 2014 at 11:47 | comment | added | joro | @GerryMyerson Indeed. Working symbolically don't think counterexamples exist for n=3 or n=4. | |
| May 27, 2014 at 11:30 | comment | added | Gerry Myerson | A smaller example is the circulant with first row $1,-1,1,0,0$. | |
| May 27, 2014 at 10:47 | history | edited | joro | CC BY-SA 3.0 |
Explained about columns
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| May 27, 2014 at 9:49 | history | answered | joro | CC BY-SA 3.0 |