  Alternating sign triangles (ASTs) have recently been introduced by Ayyer,
Behrend and the author, and it was proven that there is the same number of ASTs
with n rows as there is of nxn alternating sign matrices (ASMs). We prove a
conjecture by Behrend on a refined enumeration of ASTs with respect to a
statistic that is shown to have the same distribution as the column of the
unique 1 in the top row of an ASM. The proof of the conjecture is based on a
certain multivariate generating function of ASTs that takes the positions of
the columns with sum 1 (1-columns) into account. We also prove a curious
identity on the cyclic rotation of the 1-columns of ASTs. Furthermore, we
discuss a relation of our multivariate generating function to a formula of Di
Francesco and Zinn-Justin for the number of fully packed loop configurations
associated with a given link pattern. The proofs of our results employ the
author's operator formula for the number of monotone triangles with prescribed
bottom row. This is opposed to the six-vertex model approach that was used by
Ayyer, Behrend and the author to enumerate ASTs, and since the refined
enumeration implies the unrefined enumeration, the present paper also provides
an alternative proof of the enumeration of ASTs.
