论文标题
Hopf有序的简单复合物
Hopf monoids of ordered simplicial complexes
论文作者
论文摘要
我们从HOPF理论的角度研究了有序的成曲线和广义的Permutohedra。我们的主要对象是配备有坐标级的扩展通用定居者的向量物种中的HOPF MONOID；这种单体扩展了由Aguiar和Ardila研究的广义定向的HOPF MONOID。我们的反模型公式是无取消和不含多重性的，仅根据与多面体的局部几何形状兼容的术语支持。我们的结果是一个较大程序的一部分，以了解诸如简单复合物的地面集（例如，在移位和矩阵独立络合物上）。在这种情况下，我们表明，改变的简单络合物和破碎的电路复合物会产生Hopf单体，预计会表现出相似的行为。
We study ordered matroids and generalized permutohedra from a Hopf theoretic point of view. Our main object is a Hopf monoid in the vector species of extended generalized permutahedra equipped with an order of the coordinates; this monoid extends the Hopf monoid of generalized permutahedra studied by Aguiar and Ardila. Our formula for the antipode is cancellation-free and multiplicity-free, and is supported only on terms that are compatible with the local geometry of the polyhedron. Our result is part of a larger program to understand orderings on ground sets of simplicial complexes (for instance, on shifted and matroid independence complexes). In this vein, we show that shifted simplicial complexes and broken circuit complexes generate Hopf monoids that are expected to exhibit similar behavior.
