Eulerian pairs on Fibonacci words
Teresa X.S. Li, Charles B. Mei, Melissa Y.F. Miao
TL;DR
This paper explores Eulerian pairs on Fibonacci words using various bijections, extending the concept introduced by Sagan and Savage, and provides new insights into their combinatorial structure.
Contribution
It introduces new Eulerian pairs on Fibonacci words based on Foata's transformation, Han's bijection, and a Steingrímsson-inspired map, expanding the understanding of Fibonacci word combinatorics.
Findings
Identified Eulerian pairs on Fibonacci words using Foata's first transformation.
Constructed Eulerian pairs via Han's bijection.
Developed a new bijection inspired by Steingrímsson's work.
Abstract
Recently, Sagan and Savage introduced the notion of Eulerian pairs. In this note, we find Eulerian pairs on Fibonacci words based on Foata's first transformation or Han's bijection and a map in the spirit of a bijection of Steingr\'{\i}msson.
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