A polyomino is a finite, connected subgraph of the square-grid graph consisting of infinitely
many unit cells matched edge-to-edge, with pairs of adjacent cells forming edges of the …

A d-dimensional polycube of size n is a connected set of n cubes in d dimensions, where
connectivity is through (d− 1)-dimensional faces. In this paper, we develop a theoretical …

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 …

We develop a general framework for computing formulae enumerating polycubes of size n
which are proper in n− k dimensions (spanning all n− k dimensions), for a fixed value of k …

In this paper, we consider enumeration of d-dimensional polycubes, whose perimeter
(defined as the number of empty cells neighboring the polycube) has a fixed deviation from …

In this paper we develop a theoretical framework for computing the explicit formula
enumerating polycubes with n cubes that span n− k dimensions, for a fixed k and variable n …

A polyomino is a finite, connected subgraph of the square-grid graph consisting of infinitely
many unit cells matched edge-to-edge, with pairs of adjacent cells forming edges of the …