On the number of pancake stacks requiring four flips to be sorted
Abstract
Using existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake graph, due to the authors, is used to derive a formula for the number of signed permutations requiring 4 (burnt) pancake flips to be sorted. We furthermore provide an analogous characterization of the 9-cycles in the burnt pancake graph. Finally we present numerical evidence that polynomial formulae exist giving the number of signed permutations that require flips to be sorted, with .
Keywords
Cite
@article{arxiv.1902.04055,
title = {On the number of pancake stacks requiring four flips to be sorted},
author = {Saúl A. Blanco and Charles Buehrle and Akshay Patidar},
journal= {arXiv preprint arXiv:1902.04055},
year = {2023}
}
Comments
We have finalized for the paper for publication in DMTCS, updated a reference to its published version, moved the abstract to its proper location, and added a thank you to the referees. The paper has 27 pages, 6 figures, and 2 tables