论文标题
签名的Persutohedra，Delta-Matroids及其他
Signed permutohedra, delta-matroids, and beyond
论文作者
论文摘要
我们建立了B型置换曲面各种多种的代数几何形状与三角洲 - 摩肌的组合之间的联系。使用此连接，我们计算B型Bentrized Persutohedra的体积和晶格计数。将热带霍奇理论应用于一个新的框架“ Delta-Matroids的重言式类别”的新框架，以某些与可实现的三角洲 - 摩atroids相关的某些矢量捆绑包进行了建模，我们建立了一个像Tutte一样不变的对数型的log-mata-Mata-Matroid家族，其中包括所有delta-matroids of Realizable delta Matroids。我们的结果包括针对特殊情况的所有（普通）矩阵的新的对数毫无用处的语句。
We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized permutohedra. Applying tropical Hodge theory to a new framework of "tautological classes of delta-matroids," modeled after certain vector bundles associated to realizable delta-matroids, we establish the log-concavity of a Tutte-like invariant for a broad family of delta-matroids that includes all realizable delta-matroids. Our results include new log-concavity statements for all (ordinary) matroids as special cases.
