  Multi-parton distributions in a proton, the nonperturbative quantities needed
to make predictions for multiple scattering rates, are poorly constrained from
theory and data and must be modelled. All Monte Carlo event generators that
simulate multiple parton interactions (e.g. Pythia) contain such a model of
multi-parton PDFs. One important theoretical constraint for the case of double
parton distributions is provided by the so-called number and momentum sum
rules. In this paper we investigate to what extent the double parton
distribution functions used in the Pythia event generator obey these sum rules.
We also derive the number and momentum sum rules for the triple parton
distribution functions and discuss how one can use the Pythia code to construct
triple parton distribution functions which approximately satisfy these sum
rules.
