Proof of the monotone column permanent conjecture

Details Proof of the monotone column permanent conjecture Proof of the monotone column permanent conjecture

2010-10-13

arxiv.org/abs/1010.2565v2

Mathematics

Combinatorics

Scientific paper

Let A be an n-by-n matrix of real numbers which are weakly decreasing down each column, Z_n = diag(z_1,..., z_n) a diagonal matrix of indeterminates, and J_n the n-by-n matrix of all ones. We prove that per(J_nZ_n+A) is stable in the z_i, resolving a recent conjecture of Haglund and Visontai. This immediately implies that per(zJ_n+A) is a polynomial in z with only real roots, an open conjecture of Haglund, Ono, and Wagner from 1999. Other applications include a multivariate stable Eulerian polynomial, a new proof of Grace's apolarity theorem and new permanental inequalities.

Affiliated with

Also associated with

No associations

Rating

Proof of the monotone column permanent conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Proof of the monotone column permanent conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proof of the monotone column permanent conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226116