The Perimeter of Proper Polycubes

Abstract

We derive formulas for the number of polycubes of size $n$ and perimeter $t$ that are proper in $n-1$ and $n-2$ dimensions. These formulas complement computer based enumerations of perimeter polynomials in percolation problems. We demonstrate this by computing the perimeter polynomial for $n=12$ in arbitrary dimension $d$.

16 pages, 4 figures, 2 tables

References in corpus (1)

• Counting Lattice Animals in High Dimensions