Gill Barequet and Mira Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, Proc. 8th European Conf. on Combinatorics, Graph Theory, and Applications (EuroComb), 49, 145-151, 2015.


We develop a general framework for computing formulae enumerating polycubes of size n which are proper in n-k dimensions (spanning all dimensions), for a fixed value of k. Besides the fundamental importance of knowing the number of these simple combinatorial objects, such formulae are central in the literature of statistical physics in the study of percolation processes and the collapse of branched polymers. We re-affirm the already-proven formulae for k<4, and prove rigorously, for the first time, the formula enumerating proper n-4 dimensional polycubes.


	author = {Gill Barequet and Mira Shalah},
	title = {Automatic Proofs for Formulae Enumerating Proper Polycubes},
	booktitle = {Proceedings of the 8th European Conference on Combinatorics, Graph Theory and Applications (EuroComb)},
	venue = {Bergen, Norway},
	volume = {49},
	pages = {145--151},
	year = {2015},
	month = {August--September},