We implement an algorithm RSHT (Random Simple-Homotopy) to study the simple-homotopy types of simplicial complexes, with a particular focus on contractible spaces and on finding substructures in higher-dimensional complexes. The algorithm combines elementary simplicial collapses with pure elementary expansions. For triangulated d-manifolds with d < 7, we show that RSHT reduces to (random) bistellar flips. Among the many examples on which we test RSHT, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, (14k+1)-vertex triangulations of Bing's houses with k rooms, which all can be deformed to a point using only six pure elementary expansions.
翻译:我们实施了 RSHT 算法( Random 简单- Homotopy), 以研究简单机动型的简化复合体, 特别侧重于可承包空间和在高维复合体中寻找子结构。 该算法将初级简化式崩溃与纯基本扩展结合起来。 对于三角的d- manyflops 和 d < 7, 我们显示 RSHT 减少为( 随机) 饼干翻转。 在我们测试 RSHT 的许多例子中, 我们描述了对Abloone 的15 个垂直三角, 更一般地说, (14k+1) - 垂直三角对Bing 的房屋和 k 房间, 这些房间只能用6个纯基本扩展来变形。