Chirotopes are a common combinatorial abstraction of (planar) point sets. In this paper we investigate decomposition methods for chirotopes, and their application to the problem of counting the number of triangulations supported by a given planar point set. In particular, we generalize the convex and concave sums operations defined by Rutschmann and Wettstein for a particular family of chirotopes (which they call chains), and obtain a precise asymptotic estimate for the number of triangulations of the double circle, using a functional equation and the kernel method.

翻译：手征体是（平面）点集的一种常见组合抽象。本文研究手征体的分解方法及其在计算给定平面点集所支持三角剖分数量问题中的应用。具体而言，我们将Rutschmann和Wettstein为特定手征体族（称为链）定义的凸和与凹和运算进行推广，通过函数方程与核方法，获得了双圆点集三角剖分数的精确渐近估计。