On the refined 3-enumeration of alternating sign matrices

Details On the refined 3-enumeration of alternating sign matrices On the refined 3-enumeration of alternating sign matrices

2004-04-19

arxiv.org/abs/math-ph/0404045v2

Adv.Appl.Math. 34 (2005) 798-811

Physics

Mathematical Physics

Some comments and references added. To appear in the David Robbins memorial issue of Advances in Applied Mathematics

Scientific paper

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.

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