An Algorithm to Enumerate Grid Signed Permutation Classes

TL;DR

This paper introduces an algorithm for enumerating grid signed permutation classes, with applications to genome rearrangements, showing that certain permutation counts are polynomial and computable by the proposed method.

Contribution

The paper presents a novel algorithm for enumerating grid signed permutation classes and applies it to genome rearrangements, establishing polynomial formulas for specific permutation counts.

Findings

Enumeration of grid signed permutation classes achieved

Polynomial formulas for permutation counts with fixed prefix reversal

Algorithm applicable to genome rearrangement problems

Abstract

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are equivalent to the permutation classes that can be enumerated by polynomials. Furthermore, we apply our results to genome rearrangements and establish that the number of signed permutations with fixed prefix reversal and reversal distance is given by polynomials that can be computed by our algorithm.