Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences
Year: 2016
Type: preprint
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 $132$-$312$ avoiding permutations of given length such that two successive permutations differ by at most $2$ adjacent transpositions. Also we obtain Gray codes of strong distance $2$ for the $001$ avoiding ascent sequences and the $010$ avoiding ascent sequences of given length.
Source: arXiv (Cornell University)
Author: Tomie, Masaya
Institution: Morioka University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2923529307