%0 Journal Article
%T More refined enumerations of alternating sign matrices
%A Ilse Fischer
%A Dan Romik
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0903.5073v2