Gill Barequet and Mira Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, Video Review at the 31st Symposium on Computational Geometry (SoCG), 19-22, June 2015.

Abstract:

This video describes a general framework for computing formulae enumerating polycubes of size n which are proper in n−k dimensions (i.e., spanning all n−k dimensions), for a fixed value of k. (Such formulae are central in the literature of statistical physics in the study of percolation processes and collapse of branched polymers.) The implemented software already re-affirmed the already-proven formulae for k < 4, and proved rigorously, for the first time, the formula enumerating polycubes of size n that are proper in n−4 dimensions.

Bibtex: 

@inproceedings{VBS15,
	author = {Gill Barequet and Mira Shalah},
	title = {Automatic Proofs for Formulae Enumerating Proper Polycubes},	
	booktitle = {Video Review at the 31st Symposium on Computational Geometry (SoCG)}, 
	pages = {19--22}, 
	year = {2015},
	url = {https://youtu.be/ojNDm8qKr9A},
	venue = {Eindhoven, Netherlands},
	month = {June}, 
}