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Showing 1 to 3 of 3 for “"Fano Plane"”.
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Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7
… which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find all the maximum-sized matroids for …
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Octonions and the Exceptional Lie Algebra g_2
… a special graph with seven vertices call the Fano Plane. Next we explain the Cayley-Dickson construction, which exhibits the octonions as the set of ordered pairs of quaternions. This approach parallels the realization of the complex numbers as ordered pairs of real numbers. The rest of the …
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Cayley-Dickson Loops
… the idea of the octonion multiplication Fano plane.</p>