Real-rootedness of rook-Eulerian polynomials
Per Alexandersson, Aryaman Jal, Maena Quemener · arXiv (Cornell University) · 2025
We introduce rook-Eulerian polynomials, a generalization of the classical Eulerian polynomials arising from complete rook placements on Ferrers boards, and prove that they are real-rooted. We show that a natural context in which to interpret these rook placements is as lower intervals of $312$-avoiding permutations in the Bruhat order. We end with some variations and generalizations along this theme.