We give conditions on the numbers {φij} under which a vertexdegree-based topological index TI of the form

A permutomino of size n is a polyomino determined by particular pairs (π1, π2) of permutations of size n, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n. Here we determine

We study the problem of folding a given polyomino S into a polycube C under different folding models, allowing faces of C to be covered multiple times.

Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally, our sampler shows a limit shape for large digitally convex polyominoes. Introduction In discrete ...

Polyomino Venn (or polyVenn) diagrams are Venn diagrams whose curves are the perimeters of polyominoes drawn on the integer lattice. Minimum area polyVenn diagrams are those in which each of the 2n intersection regions, in a diagram of n polyominoes, consists of exactly one unit square. We construct minimum area polyVenn diagrams in bounding rectangles of size 2r×2c whenever r, c ≥ 2. Our const...

We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes, and show that the criterion detects some cases that are not detectable by generalized coloring arguments.