On the exhaustive generation of convex permutominoes

TL;DR

This paper introduces an algorithm for exhaustively generating convex permutominoes, a specific class of polyominoes linked to permutation pairs, with efficiency proportional to the number generated.

Contribution

It presents the first algorithm for exhaustive generation of convex permutominoes and proves its linear proportionality to the number of objects.

Findings

Algorithm efficiently generates convex permutominoes

Generation cost is proportional to the number of objects

Provides enumerative results on permutominoes

Abstract

A permutomino of size n is a polyomino determined by a pair of permutations of size n+1, such that they differ in each position. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the exhaustive generation of a particular class of permutominoes, the convex permutominoes, proving that its cost is proportional to the number of generated objects.