Timeline for The lattice of covectors of an oriented matroid
Current License: CC BY-SA 3.0
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| Jun 25, 2014 at 17:33 | comment | added | Nicholas Proudfoot | Thanks! Looking at Theorem 4.1 of the Richter-Gebert/Ziegler paper to which Benjamin linked on his blog, I see that knowing $M$ is essentially equivalent to knowing both $N$ and the oriented matroid $P$ obtained from $M$ by deleting the distinguished element. I can't put my finger on a precise statement yet, but I feel as if the passage from $M$ to $P$ involves forgetting much of the orientation data. As you noted, the passage from $M$ to $L(M)$ also involves forgetting much of the orientation data. So I hold out some hope that $M$ is determined by $L(M)$ and $N$. | |
| Jun 25, 2014 at 15:40 | history | answered | Hugh Thomas | CC BY-SA 3.0 |