  We study three-point functions of single-trace operators in the su(1|1)
sector of planar N = 4 SYM borrowing several tools based on Integrability. In
the most general configuration of operators in this sector, we have found a
determinant expression for the tree-level structure constants. We then compare
the predictions of the recently proposed hexagon program against all available
data. We have obtained a match once additional sign factors are included when
the two hexagon form-factors are assembled together to form the structure
constants. In the particular case of one BPS and two non-BPS operators we
managed to identify the relevant form-factors with a domain wall partition
function of a certain six-vertex model. This partition function can be
explicitly evaluated and factorizes at all loops. In addition, we use this
result to compute the structure constants and show that at strong coupling in
the so-called BMN regime, its leading order contribution has a determinant
expression.
