Balanced Gray Codes for Permutations and Rainbow Cycles for Associahedra
Robert Lauff, Lucca Tiemens

TL;DR
This paper constructs balanced Gray codes and rainbow cycles for permutations and associahedra, providing new combinatorial structures with applications in permutation enumeration and polyhedral graph theory.
Contribution
It introduces balanced Gray codes for permutations, rainbow cycles for permutations and associahedra, and extends existing results to new classes of combinatorial objects.
Findings
Constructed a balanced transposition Gray code for permutations.
Established rainbow cycles for permutations and associahedra.
Extended rainbow cycle results to permutahedra for all n.
Abstract
We settle the problem of constructing a balanced transposition Gray code for permutations of with . More generally, we obtain a~-rainbow cycle for the permutations of for , a notion recently introduced by Felsner, Kleist, M\"utze, and Sering. Furthermore, we extend a result of theirs by presenting a -rainbow cycle for the classical associahedron for . For even , we also construct a balanced Gray code for permutations of , using only cyclically adjacent transpositions, complementing the construction for odd by Gregor, Merino, and M\"utze. Additionally, we show that the Permutahedron admits a -rainbow cycle for all and a -rainbow cycle for odd .
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Taxonomy
TopicsGenome Rearrangement Algorithms · Advanced Combinatorial Mathematics · graph theory and CDMA systems
