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.

中文翻译：

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随机简单同伦理论

我们实现了一个算法 RSHT（随机简单同伦）来研究单纯复形的简单同伦类型，特别关注可收缩空间和在高维复形中寻找​​子结构。该算法将初等单纯塌陷与纯初等展开相结合。对于 d < 7 的三角化 d 流形，我们表明 RSHT 减少到（随机）双星翻转。在我们测试 RSHT 的众多示例中，我们描述了鲍鱼的显式 15 顶点三角剖分，更一般地说，是 Bing 拥有 k 个房间的房屋的 (14k+1) 顶点三角剖分，所有这些都可以使用只有六个纯基本展开式。