  We study the effects of the integrated galactic initial mass function (IGIMF)
and dust evolution on the abundance patterns of high redshift starburst
galaxies. In our chemical models, the rapid collapse of gas clouds triggers an
intense and rapid star formation episode, which lasts until the onset of a
galactic wind, powered by the thermal energy injected by stellar winds and
supernova explosions. Our models follow the evolution of several chemical
elements (C, N, $\alpha$-elements and Fe) both in the gas and dust phases. %The
most recent stellar yield and dust prescriptions are adopted. We test different
values of $\beta$, the slope of the embedded cluster mass function for the
IGIMF, where lower $\beta$ values imply a more top-heavy initial mass function
(IMF). The computed abundances are compared to high-quality abundance
measurements obtained in lensed galaxies and from composite spectra in large
samples of star-forming galaxies in the redshift range $2 \lesssim z \lesssim
3$. The adoption of the IGIMF causes a sensible increase of the rate of star
formation with respect to a standard Salpeter IMF, with a strong impact on
chemical evolution. We find that in order to reproduce the observed abundance
patterns in these galaxies, either we need a very top-heavy IGIMF ($\beta < 2$)
or large amounts of dust. In particular, if dust is important, the IGIMF should
have $\beta \ge 2$, which means an IMF slightly more top-heavy than the
Salpeter one. The evolution of the dust mass with time for galaxies of
different mass and IMF is also computed, highlighting that the dust amount
increases with a top-heavier IGIMF.
