Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences
Abstract
In this paper, we construct a listing for the vertices of the augmentation graph of given size, and as a consequence, we obtain a Hamiltonian cycle for the square of the augmentation graph of given size. As applications, we have a Gray code for the - avoiding permutations of given length such that two successive permutations differ by at most adjacent transpositions. Also we obtain Gray codes of strong distance for the avoiding ascent sequences and the avoiding ascent sequences of given length.
Keywords
Cite
@article{arxiv.1612.03620,
title = {Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences},
author = {Masaya Tomie},
journal= {arXiv preprint arXiv:1612.03620},
year = {2022}
}
Comments
17 pages, 1 figure. Section 3.1 and Section 4 in the previous version is in Section 3 and Section 4 in the new version. Torsten M\"utze pointed out that Theorem 3.1 was essentially proven in C.D.Savage, I. Shields and D. B. West, On the existence of Hamiltonian paths in the cover graph of M(n), Discrete Math, 262(1-3):241-252, 2003