Timeline for matroids representable over root of unity partial fields that are not the 6th root of unity partial field

7 events

when toggle format	what		by	license	comment
Jan 25, 2017 at 16:10	vote	accept	Karen Yeats
Jan 24, 2017 at 15:58	comment	added	Rudi Pendavingh		The uniform matroid $U_{2,4}$ cannot be represented over $\{1,-1,i,-1\}$. Therefore, if $M$ is representable over $\{1,-1,i,-1\}$, then $M$ cannot have $U_{2,4}$ as a minor, hence $M$ is binary. But since such $M$ is also sixth-root, $M$ is ternary as well. Binary+ternary = regular.
Jan 23, 2017 at 15:39	comment	added	Karen Yeats		Thanks Rudi. That is very helpful. Why is it true?
Jan 19, 2017 at 21:52	history	edited	Rudi Pendavingh	CC BY-SA 3.0	added 1 character in body
Jan 19, 2017 at 21:41	comment	added	Rudi Pendavingh		$M$ is representable over $\{1,-1, i,-i\}$ if and only if $M$ is regular.
Jan 16, 2017 at 18:59	comment	added	Karen Yeats		I think that explains very well why the 6th root of unity matroids are so important. Still, matroid classes like the {1,-1,i,-i} partial field representable ones would live inside the 6th root of unity matroids and it isn't clear to me what that subclass would look like.
Jan 14, 2017 at 19:26	history	answered	Rudi Pendavingh	CC BY-SA 3.0