Counting the spanning trees of the 3-cube using edge slides

Details Counting the spanning trees of the 3-cube using edge slides Counting the spanning trees of the 3-cube using edge slides

2011-09-29

arxiv.org/abs/1109.6393v1

Mathematics

Combinatorics

15 pages, 9 figures

Scientific paper

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 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, and we discuss the possibilities and difficulties of extending our approach to n>3.

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