带符号排列多面体、delta-拟阵及其他
Signed permutohedra, delta-matroids, and beyond
AI总结：
本文建立了B型排列多面体环面簇的代数几何与delta-拟阵组合学的联系，计算了B型广义排列多面体的体积和格点计数，并利用热带Hodge理论确立了包含可实现delta-拟阵在内的该类拟阵的类Tutte不变量的对数凹性。
摘要：
我们建立了B型排列多面体环面簇的代数几何与delta-拟阵组合学之间的联系。利用这一联系，我们计算了B型广义排列多面体的体积和格点计数。将热带Hodge理论应用于“delta-拟阵的示性类”的新框架（该框架仿照与可实现delta-拟阵相关的某些向量丛构建），我们确立了一大类delta-拟阵（包含所有可实现delta-拟阵）的类Tutte不变量的对数凹性。我们的结果包含了对所有（普通）拟阵的新的对数凹性命题作为特例。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
