A formula for the doubly-refined enumeration of alternating sign matrices

Details A formula for the doubly-refined enumeration of alternating sign matrices A formula for the doubly-refined enumeration of alternating sign matrices

2009-06-18

arxiv.org/abs/0906.3405v1

Mathematics

Combinatorics

10 pages, 4 figures

Scientific paper

Zeilberger proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey, for the number of alternating sign matrices with given top row. Stroganov proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik considered a different kind of "doubly-refined enumeration" where one counts alternating sign matrices with given top two rows, and obtained partial results on this enumeration. In this paper we continue the study of the doubly-refined enumeration with respect to the top two rows, and use Stroganov's formula to prove an explicit formula for these doubly-refined enumeration numbers.

Affiliated with

Also associated with

No associations

Rating

A formula for the doubly-refined enumeration of alternating sign matrices 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 A formula for the doubly-refined enumeration of alternating sign matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A formula for the doubly-refined enumeration of alternating sign matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725714