@inproceedings{b320dcf0d6644318a45e36240afa9d5f,
title = "Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations",
abstract = "Wiggly permutations were introduced by Bapat and Pilaud (Wigglyhedron Mathematische Zeitschrift 2025). We positively answer one of their conjectures by finding a Hamilton path in the wiggly flip graph that is isomorphic to the wigglyhedron. Our path provides a Gray code in which successive wiggly permutations are obtained by a single jump or hop, meaning that one or two consecutive symbols move past some number of smaller symbols. The Gray code has a simple greedy description that produces a recursive zig-zag pattern reminiscent of plain changes for permutations. More broadly, our results extend Algorithm J and the series of papers on zig-zag languages initiated by Hartung, Hoang, M{\"u}tze and Williams (Combinatorial Generation via Permutation Languages SODA 2020). Finally, we use wiggly changes as the basis for an O(n)-time delay generation algorithm.",
keywords = "Gray code, Hamilton path, combinatorial generation, flip graph, generation algorithm, pattern avoidance, permutahedron, permutations, wiggly permutations, wigglyhedron",
author = "Vincent Pilaud and Aaron Williams",
note = "Publisher Copyright: {\textcopyright} Vincent Pilaud and Aaron Williams.; 19th International Symposium on Algorithms and Data Structures, WADS 2025 ; Conference date: 11-08-2025 Through 15-08-2025",
year = "2025",
month = aug,
day = "29",
doi = "10.4230/LIPIcs.WADS.2025.46",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Pat Morin and Eunjin Oh",
booktitle = "19th International Symposium on Algorithms and Data Structures, WADS 2025",
}