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・ Sylvia Barlag
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Sylvester matroid
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Sylvester matroid : ウィキペディア英語版
Sylvester matroid
In matroid theory, a Sylvester matroid is a matroid in which every pair of elements belongs to a three-element circuit (a ''triangle'') of the matroid.〔.〕〔.〕
==Example==
The n-point line (i.e., the rank 2 uniform matroid on n elements, U{}^2_n) is a Sylvester matroid because every pair of elements is a basis and every triple is a circuit.
A Sylvester matroid of rank three may be formed from any Steiner triple system, by defining the lines of the matroid to be the triples of the system. Sylvester matroids of rank three may also be formed from Sylvester–Gallai configurations, configurations of points and lines (in non-Euclidean spaces) with no two-point line. For example, the Fano plane and the Hesse configuration give rise to Sylvester matroids with seven and nine elements respectively, and may be interpreted either as Steiner triple systems or as Sylvester–Gallai configuration.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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