标题： 一种高效的平坦折叠枚举：随机单顶点折纸研究 显示英文标题

标题： An Efficient Enumeration of Flat-Foldings : Study on Random Single Vertex Origami

摘要： 本文涉及的主题包括对随机折纸图的平坦折叠总数的近似计数/评估，对各种实例的平均值的评估，获取一般折纸图的强制集，以及评估平均计算复杂度。 提出了一种使用物理模型和高效大小缩减方法来解决上述问题的方法。 利用统计力学模型和基于该模型的近似枚举数值方法，我们给出了具有围绕中心顶点的随机角度宽度的单顶点折纸图平坦折叠总数的近似枚举结果，并获得了其大小依赖性，以进行无限大小极限的渐近预测。 此外，还从组织物理模型中包含项的角度出发，提供了关于由于禁止它们穿透而引起的局部堆叠顺序链式确定的展望。 基于上述观点，讨论了高效解决平坦折叠确定或枚举问题的方法。 这被认为与强制集密切相关。 显示英文摘要

摘要： This paper deals with themes such as approximate counting/evaluation of the total number of flat-foldings for random origami diagrams, evaluation of the values averaged over various instances, obtaining forcing sets for general origami diagrams, and evaluation of average computational complexity. An approach to the above problems using a physical model and an efficient size reduction method for them is proposed. Using a statistical mechanics model and a numerical method of approximate enumeration based on it, we give the result of approximate enumeration of the total number of flat-foldings of single-vertex origami diagram with random width of angles gathering around the central vertex, and obtain its size dependence for an asymptotic prediction towards the limit of infinite size. In addition, an outlook with respect to the chained determination of local stacking orders of facets caused by the constraint that prohibits the penetration of them is also provided from the viewpoint of organizing the terms included in the physical model. A method to efficiently solve the problem of the determination or enumeration of flat-foldings is discussed based on the above perspectives. This is thought to be closely related to forcing sets.