On the refined 3-enumeration of alternating sign matrices

F. Colomo, A. G. Pronko

Published 2004-04-19, updated 2004-11-25Version 2

An explicit expression for the numbers $A(n,r;3)$ describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, $A(n,r;3)$'s are represented as 1-fold sums which can also be written in terms of terminating ${}_4F_3$ series of argument 1/4.