Counting the spanning trees of the 3-cube using edge slides
Combinatorics
2012-10-03 v2
Abstract
We give a direct combinatorial proof of the known fact that the 3-cube has 384 spanning trees, using an "edge slide" operation on spanning trees. This gives an answer in the case n=3 to a question implicitly raised by Stanley. Our argument also gives a bijective proof of the n=3 case of a weighted count of the spanning trees of the n-cube due to Martin and Reiner.
Cite
@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}
}
Comments
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