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 Feb 12 awarded Editor Feb 12 revised On duality on finite projective planes added 1 characters in body Feb 11 answered On duality on finite projective planes Nov 16 comment Constructing a field from a spherical building Good references are the addendum to "Moufang buildings" of Tits' book "Buildings of spherical type and finite BN-pairs", The book "Moufang generalized polygons" of Tits and Weiss, or the book "The structure of spherical buildings" by Weiss. Nov 15 answered Constructing a field from a spherical building Aug 9 awarded Yearling Jul 5 comment Tetris-like falling sticky disks I'd suspect if you zoom in enough they aren't connected anymore. Jul 5 comment Tetris-like falling sticky disks As far as I understand there are no cycles in the picture from the original post (with probability 1). This as the values on the $x$-axis for which adding a disk would form a cycle is a finite discrete set, and hence a null set. Jun 20 answered Good books on problem solving / math olympiad May 6 answered The Weyl group of $SL(2, F)$ Apr 10 comment Rock-paper-scissors… One way of approaching this problem would be to decompose the complete graph into cycles. Adding orientation to these cycles gives you a balanced tournament. Moreover each balanced tournament arises in this way. There is a lot of literature on such decompositions. For example decompositions into 3-cycles are equivalent with Steiner triple systems. Apr 10 comment Rock-paper-scissors… "balanced" seems to be the correct terminology, see en.wikipedia.org/wiki/Directed_graph Apr 10 comment Commutator table for Chevalley group G_2 Would the relations between 6 or 7 consecutive root groups of $G_2(q)$ be sufficient for your purposes? I can give you that if you want. Apr 9 comment (weak?) BN-Pair / Tits System for Sporadic Groups Just noting: The rank 1 situation can be formalized to what is called "split BN-pair of rank one" or "Moufang sets" (which do not include the Mathieu groups). See for example this survey by Tom De Medts and Yoav Segev: cage.UGent.be/~tdemedts/preprints/moufsets.pdf . Mar 27 awarded Critic Feb 27 awarded Commentator Jan 30 comment How to minimize the length of a graph connecting n points in $\mathbb{R}^3$ For $n=4$ the vertices of a tetrahedron would be optimal. Also note that you can rephrase your problem to a sphere packing problem. Jan 18 comment Sums of Unitary Matrices A way to picture it geometrically: consider the line $x_1 = x_2 = \dots x_n$ (the $x_i$ being the coordinates of the vector space) and the rotation of 180 degrees around this line. The sum of a vector and his image rotation then lies on this line, from which one then can derive that the sum of the identity matrix and the matrix corresponding with the rotation is of the form $\lambda J$. Jan 17 answered Embedding of finite groups in Symmetric Groups Jan 4 comment Selecting two random points inside a sphere which are a fixed distance apart Are you looking for a theoretical or a computational answer?