Logarithmic concavity of Schur and related polynomials

DOI10.1090/tran/8606OpenAlexW4206704953WikidataQ113006631 ScholiaQ113006631MaRDI QIDQ5082408

June Huh, Avery St. Dizier, Karola Mészáros, Jacob P. Matherne

Publication date: 16 June 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.09633

zbMATH Keywords

log-concavitySchur polynomialsweight multiplicitiesLorentzian polynomials

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Determinantal varieties (14M12)

Related Items

Inclusion-exclusion on Schubert polynomials, The metric space of limit laws for $q$-hook formulas, Partial symmetries of iterated plethysms, Double Schubert polynomials do have saturated Newton polytopes, Multivariate correlation inequalities for \(P\)-partitions, On the convexity of general inverse \(\sigma_k\) equations, On Hodge-Riemann cohomology classes, Column-convex matrices, \(G\)-cyclic orders, and flow polytopes, Geometric and functional inequalities for log-concave probability sequences, Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones, Combinatorics and Hodge theory

Cites Work

• An invitation to the generalized saturation conjecture
• Gröbner geometry of Schubert polynomials
• Chains in the Bruhat order
• Kostant partitions functions and flow polytopes
• Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups
• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
• Schubert polynomials and Bott-Samelson varieties
• Key polynomials and a flagged Littlewood-Richardson rule
• Schubert polynomials as integer point transforms of generalized permutahedra
• Example of a non-log-concave Duistermaat-Heckman measure
• A vector partition function for the multiplicities of \(\mathfrak{sl}_k\mathbb C\)
• Logarithmic convexity of push-forward measures
• From generalized permutahedra to Grothendieck polynomials via flow polytopes
• Logarithmic concavity for morphisms of matroids
• Simplicial generation of Chow rings of matroids
• Lorentzian polynomials
• Newton polytopes in algebraic combinatorics
• Newton polytopes and symmetric Grothendieck polynomials
• Zero-one Schubert polynomials
• Multivariate stable polynomials: theory and applications
• Permutohedra, Associahedra, and Beyond
• On multivariate Newton-like inequalities
• Discrete Convex Analysis
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid
• Convex Bodies The Brunn-MinkowskiTheory
• Counterexamples to Okounkov’s log-concavity conjecture
• Schur positivity and Schur log-concavity
• Theory of Matroids
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