More refined enumerations of alternating sign matrices

Details More refined enumerations of alternating sign matrices More refined enumerations of alternating sign matrices

2009-03-29

arxiv.org/abs/0903.5073v2

Mathematics

Combinatorics

38 pages; added references and made minor changes to the introduction; source files now inlcude the Mathematica package Refine

Scientific paper

We study a further refinement of the standard refined enumeration of alternating sign matrices (ASMs) according to their first two rows instead of just the first row, and more general "d-refined" enumerations of ASMs according to the first d rows. For the doubly-refined case of d=2, we derive a system of linear equations satisfied by the doubly-refined enumeration numbers A_{n,i,j} that enumerate such matrices. We give a conjectural explicit formula for A_{n,i,j} and formulate several other conjectures about the sufficiency of the linear equations to determine the A_{n,i,j}'s and about an extension of the linear equations to the general d-refined enumerations.

Affiliated with

Also associated with

No associations

Rating

More refined enumerations 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 More refined enumerations of alternating sign matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and More refined enumerations of alternating sign matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-202521