Extended formulations of $(k,l)$-sparsity matroids defined on graphs with n vertices and m edges are investigated by Iwata et al. [Extended formulations for sparsity matroids, Math. Program. 158 (2016), pp. 565–574]. This note interprets results on $(k,l)$-lower-truncated transversal polymatroids by the first author in 1983, from the viewpoint of extended formulations, and shows the same $O(mn)$ bound when $k\ge l$ and a better bound $O(m^2)$ when k<l. A unified polymatroidal approach is given to derive more general understanding.

中文翻译：

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下截头横向多类拟阵的扩展配方

的扩展配方 $（ķ，升）$Iwata等人研究了在具有n个顶点和m个边的图形上定义的稀疏拟阵。[稀疏拟阵的扩展公式，数学。程序。158（2016），第565–574页]。本说明解释了以下结果$（ķ，升）$第一作者于1983年从扩展配方的角度出发，将其截短 $Ø（米ñ）$ 绑定时间 $ķ\ge 升$ 和更好的界限 $Ø（{米}^{\mathrm{2个}}）$当k < l时。给出了统一的多面体方法来获得更一般的理解。