Matroid base polytope decomposition II: Sequences of hyperplane splits
Matroid base polytope decomposition II: Sequences of hyperplane splits
复制标题
拟阵基多胞体分解 II：超平面分裂序列
DOI：
10.1016/j.aam.2013.11.003
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
J. R. Alfonsín
中科院分区：
文献类型：
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作者：
Vanessa Chatelain;J. R. Alfonsín
这是一个延续的早期文件Chatelain等人。（2011）[3]关于拟阵基多胞形分解。我们将给出拟阵M的基多胞形P（M）具有超平面分裂序列的充分条件。这就产生了P（M）的分解，对于无穷多个拟阵M，P（M）有两个或多个部分。我们还给出了三阶拟阵M的欧几里得表示的必要条件，以使P（M）分解为2或3个部分。最后，证明了P（M1 <$M2）有超平面分裂序列，如果P（M1）或P（M2）也有超平面分裂序列.
This is a continuation of an early paper Chatelain et al.(2011)[3] about matroid base polytope decomposition. We will present sufficient conditions on a matroid M so its base polytope P (M) has a sequence of hyperplane splits. These yield to decompositions of P (M) with two or more pieces for infinitely many matroids M. We also present necessary conditions on the Euclidean representation of rank three matroids M for the existence of decompositions of P (M) into 2 or 3 pieces. Finally, we prove that P (M 1⊕ M 2) has a sequence of hyperplane splits if either P (M 1) or P (M 2) also has a sequence of hyperplane splits.