关于需要四次翻转才能排序的煎饼栈数量
离散数学
2023-06-22 v4 组合数学
摘要
利用煎饼图中7-环和8-环的已有分类结果，我们确定了需要4次煎饼翻转（前缀反转）才能排序的排列数。基于作者提出的烧焦煎饼图中8-环的类似刻画，我们推导了需要4次（烧焦）煎饼翻转才能排序的有符号排列数的公式。此外，我们提供了烧焦煎饼图中9-环的类似刻画。最后我们给出了数值证据，表明存在多项式公式可给出需要次翻转才能排序的有符号排列数，其中。
引用
@article{arxiv.1902.04055,
title = {On the number of pancake stacks requiring four flips to be sorted},
author = {Saúl A. Blanco and Charles Buehrle and Akshay Patidar},
journal= {arXiv preprint arXiv:1902.04055},
year = {2023}
}
备注
We have finalized for the paper for publication in DMTCS, updated a reference to its published version, moved the abstract to its proper location, and added a thank you to the referees. The paper has 27 pages, 6 figures, and 2 tables