Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The \(\varGamma \)-extension operation on binary matroids is a generalization of the point-addition operation. In this paper, for a given binary matroid M we characterize the closure operator and the flats of the \(\varGamma \)-extension binary matroid \(M^X\) in terms of the closure operator of original binary matroid M.

中文翻译：

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$${\pmb \varGamma }$$ Γ -extension matroids 的闭包算子和平面

Slater 引入了图上的点加运算来表征 4 连通图。二元拟阵上的\(\varGamma \) 扩展运算是点加运算的推广。在本文中，对于给定的二元拟阵M，我们根据原始二元拟阵M的闭合算子来刻画 \(\varGamma \) -扩展二元拟阵\(M^X\)的闭包算子和平面。