连接3-流形三角剖分与基本移动的单峰序列
Connecting 3-manifold triangulations with unimodal sequences of elementary moves
AI总结：
本文证明同一3-流形的任意两个单顶点三角剖分（各含至少两个四面体）可由2-3和2-0移动的单峰序列连接，并实现算法进行实验验证。
摘要：
计算3-流形拓扑学中的一个关键结果是，同一3-流形的任意两个三角剖分都可以通过有限序列的双星翻转（也称为Pachner移动）相连接。该结果的一个局限在于，人们对这个序列的结构知之甚少；对结构有更多了解可能有助于证明和算法。受此启发，我们考虑“单峰”的移动序列，即它们分为两部分：首先，单调增加三角剖分大小的序列；其次，单调减小大小的序列。我们证明，同一3-流形的任意两个单顶点三角剖分，每个至少包含两个四面体，都可以通过2-3和2-0移动的单峰序列相连接。我们还研究了单峰序列的实际效用；具体来说，我们实现了一个寻找此类序列的算法，并使用该算法进行了一些详细的计算实验。
英文摘要：
A key result in computational 3-manifold topology is that any two triangulations of the same 3-manifold are connected by a finite sequence of bistellar flips, also known as Pachner moves. One limitation of this result is that little is known about the structure of this sequence; knowing more about the structure could help both proofs and algorithms. Motivated by this, we consider sequences of moves that are "unimodal" in the sense that they break up into two parts: first, a sequence that monotonically increases the size of the triangulation; and second, a sequence that monotonically decreases the size. We prove that any two one-vertex triangulations of the same 3-manifold, each with at least two tetrahedra, are connected by a unimodal sequence of 2-3 and 2-0 moves. We also study the practical utility of unimodal sequences; specifically, we implement an algorithm to find such sequences, and use this algorithm to perform some detailed computational experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
