利用边滑动计数 3-立方体的生成树
组合数学
2012-10-03 v2
摘要
我们利用生成树上的“边滑动”操作，给出了 3-立方体拥有 384 棵生成树这一已知事实的直接组合证明。这回答了 Stanley 隐含提出的关于 n=3 情形的问题。我们的论证还给出了 Martin 和 Reiner 提出的 n-立方体生成树加权计数在 n=3 情形下的双射证明。
引用
@article{arxiv.1109.6393,
title = {Counting the spanning trees of the 3-cube using edge slides},
author = {Christopher Tuffley},
journal= {arXiv preprint arXiv:1109.6393},
year = {2012}
}
备注
17 pages, 9 figures. v2: Final version as published in the Australasian Journal of Combinatorics. Section 5 shortened and restructured; references added; one figure added; some typos corrected; additional minor changes in response to the referees' comments