2024/06/13 by Kassie Archer, Archer, Kassie, Aaron Geary +1
Arts and Humanities · #Language, Linguistics, Cultural Analysis
paper · pdf · doi:10.48550/arxiv.2406.09369
We consider a few special cases of the more general question: How many permutations π\inSn have the property that π2 has j descents for some j? In this paper, we first enumerate Grassmannian permutations π by the number of descents in π2. We then consider all permutations whose square has exactly one descent, fully enumerating when the descent is "small" and providing a lower bound in the general case. Finally, we enumerate permutations whose square or cube has the maximum number of descents, and finish the paper with a few future directions for study.