Skip to Main content Skip to Navigation
Conference papers

On the Monotone Column Permanent conjecture

Abstract : We discuss some recent progress on the Monotone Column Permanent (MCP) conjecture. We use a general method for proving that a univariate polynomial has real roots only, namely by showing that a corresponding multivariate polynomial is stable. Recent connections between stability of polynomials and the strong Rayleigh property revealed by Brändén allows for a computationally feasible check of stability for multi-affine polynomials. Using this method we obtain a simpler proof for the $n=3$ case of the MCP conjecture, and a new proof for the $n=4$ case. We also show a multivariate version of the stability of Eulerian polynomials for $n \leq 5$ which arises as a special case of the multivariate MCP conjecture.
Complete list of metadata

Cited literature [7 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185436
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, August 20, 2015 - 11:09:41 AM
Last modification on : Friday, June 28, 2019 - 2:48:03 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:44:46 AM

File

dmAK0137.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

James Haglund, Mirkó Visontai. On the Monotone Column Permanent conjecture. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.443-454, ⟨10.46298/dmtcs.2743⟩. ⟨hal-01185436⟩

Share

Metrics

Record views

23

Files downloads

348