CGGC Seminar: Gill Barequet (Computer Science, Technion)
A $d$-dimensional polycube is a connected set of $d$-dimensional cubes on an
orthogonal lattice, where connectivity is through $(d-1)$-dimensional faces.
A polycube is said to be proper in $d$ dimensions if it spans all the $d$
dimensions, that is, the convex hull of the centers of all its cubes is
We prove a few new formulae for the numbers of (proper and total) polycubes,
and show that (2d-3)e + O(1/d) is the asymptotic growth rate of the number
of $d$-dimensional polycube.
Joint work with Ronnie Barequet (Math and Computer Science, Tel Aviv Univ.).