Timeline for Representability of matroids over $\mathbb R$
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2021 at 11:30 | comment | added | Tony Huynh | I am not sure what the definition of managable is, but given a matroid $M$ of size $n$ and rank $r$, you can introduce $nr$ real variables and use the fact that the determinant is a polynomial. This defines a semi-algebraic set $S$ such that $M$ is real-representable if and only if $S$ is non-empty. | |
| Jun 22, 2015 at 7:32 | vote | accept | Andreas Thom | ||
| Dec 4, 2010 at 13:03 | comment | added | Andreas Thom | You said that real-presentability is decidable. Has this been used for anything so far? I mean, is there a managable $\mathbb R$-algebra $A(M)$ that one can construct out of a matroid $M$, so that $M$ is real-representable if and only if $-1$ is not a sum of squares in $A(M)$ (or something like this). | |
| Dec 3, 2010 at 16:58 | history | edited | Tony Huynh | CC BY-SA 2.5 |
added 630 characters in body; deleted 19 characters in body
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| Dec 3, 2010 at 16:52 | comment | added | Andreas Thom | Thanks. This is somehow saying that there cannot be any positive answers to my question using the language of minors etc. Is there any positive result using different terms? | |
| Dec 3, 2010 at 15:51 | history | answered | Tony Huynh | CC BY-SA 2.5 |