Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences

Masaya Tomie

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arXiv · 1612.03620

Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences

Masaya Tomie

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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.

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Masaya Tomie. 2016-12-12. Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences. https://arxiv.org/abs/1612.03620

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