论文标题
双重基质多型和独立复合物的内部活性
Dual matroid polytopes and internal activity of independence complexes
论文作者
论文摘要
炮击顺序是一种无处不在的工具，用于了解细胞复合物的不变性。已经付出了巨大的努力来开发技术来决定何时可以进行壳。但是，经验证据表明，某些炮击顺序比其他炮击更好。在本文中，我们探讨了在Matroid独立复合体的情况下进行这种现象。基于双重矩阵多面体和独立络合物之间的可撒性之间的新关系，我们概述了一种系统的方法来调查和比较不同的炮击顺序。我们解释了我们的新工具如何重铸和加深各种古典结果，并提出了新的启发式方法，并提出了针对西蒙和斯坦利引起的两个旧猜想的新启发式方法。此外，我们提供了免费的软件，可用于尝试这些新的几何思想。
Shelling orders are a ubiquitous tool used to understand invariants of cell complexes. Significant effort has been made to develop techniques to decide when a given complex is shellable. However, empirical evidence shows that some shelling orders are better than others. In this article, we explore this phenomenon in the case of matroid independence complexes. Based on a new relation between shellability of dual matroid polytopes and independence complexes, we outline a systematic way to investigate and compare different shellings orders. We explain how our new tools recast and deepen various classical results to the language of geometry, and suggest new heuristics for addressing two old conjectures due to Simon and Stanley. Furthermore, we present freely available software which can be used to experiment with these new geometric ideas.
