Remarks on the $α$--permanent

Details Remarks on the $α$--permanent Remarks on the $α$--permanent

2009-12-05

arxiv.org/abs/0912.1018v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

We recall Vere-Jones's definition of the $\alpha$--permanent and describe the connection between the (1/2)--permanent and the hafnian. We establish expansion formulae for the $\alpha$--permanent in terms of partitions of the index set, and we use these to prove Lieb-type inequalities for the $\pm\alpha$--permanent of a positive semi-definite Hermitian $n\times n$ matrix and the $\alpha/2$--permanent of a positive semi-definite real symmetric $n\times n$ matrix if $\alpha$ is a nonnegative integer or $\alpha\ge n-1$. We are unable to settle Shirai's nonnegativity conjecture for $\alpha$--permanents when $\alpha\ge 1$, but we verify it up to the $5\times 5$ case, in addition to recovering and refining some of Shirai's partial results by purely combinatorial proofs.

Affiliated with

Also associated with

No associations

Rating

Remarks on the $α$--permanent 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 Remarks on the $α$--permanent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Remarks on the $α$--permanent will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-706500