Six bijections between deco polyominoes and permutations

TL;DR

This paper introduces six bijections between deco polyominoes and permutations, revealing new correspondences between their classical statistics and providing a combinatorial framework for their enumeration.

Contribution

It presents six novel bijections linking deco polyominoes and permutations, enhancing understanding of their combinatorial properties and statistical correspondences.

Findings

Six bijections between deco polyominoes and permutations

New correspondences between classical statistics on both structures

Enumeration of deco polyominoes according to directed height

Abstract

In this paper we establish six bijections between a particular class of polyominoes, called deco polyominoes, enumerated according to their directed height by n!, and permutations. Each of these bijections allows us to establish different correspondences between classical statistics on deco polyominoes and on permutations.