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Mar 18, 2016 at 17:30 vote accept HenrikRüping
Mar 17, 2016 at 21:18 answer added HenrikRüping timeline score: 2
Mar 3, 2016 at 8:30 comment added მამუკა ჯიბლაძე Nice question. Maximal rank of $\cdot r$ seems to be $2^{n-1}-2^{\lceil\frac{n-1}2\rceil}$, attainable at $x_1x_2+x_3x_4+...$ (while the equality would give rank $2^{n-1}$).
Mar 3, 2016 at 1:45 comment added HenrikRüping I wrote a computer program that confirms this for $n\le 4$. It is brute force and runs over all $2^{2^n}$ elements in the exterior algebra so without any optimization bigger $n$ seem to be hopeless.
Mar 2, 2016 at 2:06 history asked HenrikRüping CC BY-SA 3.0