  Given an oriented link in the 3-sphere, the Euler characteristic of its link
Floer homology is known to coincide with its multivariate Alexander polynomial,
an invariant only defined up to a sign and powers of the variables. In this
paper, we get rid of this ambiguity by proving that this Euler characteristic
is equal to the so-called Conway function, the representative of the
multivariate Alexander polynomial introduced by Conway in 1970 and explicitly
constructed by Hartley in 1983. This is achieved by creating a model of the
Conway function adapted to rectangular diagrams, which is then compared to the
Euler characteristic of the combinatorial version of link Floer homology.
