Proof of the Monotone Column Permanent Conjecture

DOI10.1007/978-3-0348-0142-3_5zbMath1252.15007arXiv1010.2565OpenAlexW1494524200MaRDI QIDQ2911818

David G. Wagner, Mirkó Visontai, Petter Brändén, James Haglund

Publication date: 3 September 2012

Published in: Notions of Positivity and the Geometry of Polynomials (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2565

zbMATH Keywords

permanentnegative associationRayleighEulerian polynomialstable polynomialFerrers matrixGrace's apolarity theoremonly real rootsstrongly Rayleigh

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Determinants, permanents, traces, other special matrix functions (15A15) Zero sets of holomorphic functions of several complex variables (32A60)

Related Items (9)

Norm-constrained determinantal representations of multivariable polynomials ⋮ Multivariate stable Eulerian polynomials on segmented permutations ⋮ Peaks are preserved under run-sorting ⋮ Stable multivariate Eulerian polynomials and generalized Stirling permutations ⋮ Peaks are preserved under run-sorting (extended abstract) ⋮ Multivariate Eulerian Polynomials and Exclusion Processes ⋮ Statistics on multipermutations and partial \(\gamma\)-positivity ⋮ Log-concavity of asymptotic multigraded Hilbert series ⋮ New permanent approximation inequalities via identities

Cites Work

• A multiindexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences
• The Lee--Yang and Pólya--Schur programs. I: Linear operators preserving stability
• Negatively correlated random variables and Mason's conjecture for independent sets in matroids
• Van der Waerden/Schrijver-Valiant like conjectures and stable (aka hyperbolic) homogeneous polynomials: one theorem for all
• Further investigation involving rook polynomials with only real zeros
• Polynomials with the half-plane property and matroid theory
• A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions
• Multivariate stable polynomials: theory and applications
• Multivariate Pólya-Schur classification problems in the Weyl algebra
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