Polycubes with Small Perimeter Defect
Andrei Asinowski, Gill Barequet, Yufei Zheng · Society for Industrial and Applied Mathematics eBooks · 2018
A polycube is a face-connected set of cubical cells on ℤ3. To-date, no formulae enumerating polycubes by volume (number of cubes) or perimeter (number of empty cubes neighboring the polycube) are known. We present a few formulae enumerating polycubes with a fixed deviation from the maximum possible perimeter.