For even n, a carefully chosen sequence of vectors makes the spectrahedral relaxation bound for Eulerian polynomial roots exceed the univariate bound by asymptotically (3/8)(9/8)^{n/2}.
Real-rootedness of rook-Eulerian polynomials
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets
For even n, a carefully chosen sequence of vectors makes the spectrahedral relaxation bound for Eulerian polynomial roots exceed the univariate bound by asymptotically (3/8)(9/8)^{n/2}.