论文标题
简单复合物和theta多项式的三角剖分
Triangulations of simplicial complexes and theta polynomials
论文作者
论文摘要
斯坦利已经开发了简单复合物三角剖分的列举理论。在他的理论中，关键作用是由当地的$ h $ h $多项式对单纯形成的。本文开发了一种平行的理论，其中局部$ h $ - 多项式的作用是由更简单的不变的，即theta多项式的。这允许人们从theta多项式的相应特性中推断出$ h $ h $ polynemials的单形成性和伽马阳性性能，在这里进行了一些详细的研究。要提到一种具体的应用，$ h $ - 多种物质对任何简单同源性球体的三角剖分被证明是伽马阳性的，因此在新的特殊情况下确认了Gal的猜想。
An enumerative theory of triangulations of simplicial complexes has been developed by Stanley. A key role in his theory is played by the local $h$-polynomial of a triangulation of a simplex. This paper develops a parallel theory, in which the role of the local $h$-polynomial is played by a simpler invariant, namely the theta polynomial. This allows one to deduce unimodality and gamma-positivity properties of $h$-polynomials of triangulations of simplicial complexes from corresponding properties of theta polynomials, which are studied here in some detail. To mention one concrete application, the $h$-polynomial of the antiprism triangulation of any simplicial homology sphere is shown to be gamma-positive, thus confirming Gal's conjecture in a new special case.
