Rook-Eulerian polynomials of Ferrers boards are real-rooted, with an interlacing refinement, and complete rook placements correspond to Bruhat lower intervals of 312-avoiding permutations.
Rook poset equivalence of F errers boards
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Real-rootedness of rook-Eulerian polynomials
Rook-Eulerian polynomials of Ferrers boards are real-rooted, with an interlacing refinement, and complete rook placements correspond to Bruhat lower intervals of 312-avoiding permutations.