Counting the spanning trees of the 3-cube using edge slides - Tuffley CP (http://ajc.maths.uq.edu.au/pdf/54/ajc_v54_p189.pdf, 2012)
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.
Keywords: 0101 Pure Mathematics; 0103 Numerical and Computational Mathematics; 0802 Computation Theory and Mathematics