标题： 偏序集、多面体和拟阵的连续组合学初探 显示英文标题

标题： A glimpse into continuous combinatorics of posets, polytopes, and matroids

摘要： 这是一篇既具有阐述性又具有研究性的论文，在本文中我们主张对有限偏序集、凸多面体、定向拟阵、子空间排列、有限单纯复形和其他组合结构的连续类比进行系统研究。 其中的示例包括一类“连续凸多面体”的欧拉公式（由Kalai和Wigderson提出猜想），一类“连续拟阵”的对偶性结果，格拉斯曼偏序集中理想欧拉特征数的计算（与Gian-Carlo Rota的问题相关），拓扑偏序集的“同伦补公式”的阐述及其与Kallel和Karoui关于“加权重心空间”的结果的关系，以及Vassiliev关于奇异点单纯分解的猜想。 我们还包含了一个基于将空间图解释为连续偏序集的指标不等式（Sarkaria不等式）的扩展。 显示英文摘要

摘要： This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and other combinatorial structures. Among the illustrative examples are an Euler formula for a class of `continuous convex polytopes' (conjectured by Kalai and Wigderson), a duality result for a class of `continuous matroids', a calculation of the Euler characteristic of ideals in the Grassmannian poset (related to a problem of Gian-Carlo Rota), an exposition of the `homotopy complementation formula' for topological posets and its relation to the results of Kallel and Karoui about `weighted barycenter spaces' and a conjecture of Vassiliev about simplicial resolutions of singularities. We also include an extension of the index inequality (Sarkaria's inequality) based on interpreting diagrams of spaces as continuous posets.