[en] In this article, we have provided formulae for the calculation of the number of partitions with conditions on the maximum fragment size, with conditions on the minimum fragment size and with conditions on both the minimum and the maximum fragment size. To demonstrate these formulae, the notion of complementary partitions was introduced. The constrained partition numbers are notably useful in the analysis of nuclear multifragmentation. Moretto and collaborators have introduced an elegant combinatorial procedure to isolate rare events corresponding to the fragmentation of the atomic nucleus in a number of nearly equal size IMF (fragments with charge greater or equal to Z_min) supplemented by light fragments (fragments with charge less than or equal to Z_min - 1). This procedure requires the evaluation of the number of partitions corresponding to a given sum (Z_imf) of the charges of a given number (M) of IMF. This number of partitions is given as _ZminN(Z_imf,M)^Z_min-1N(Z_tot - Z_imf). The total number of partitions can be evaluated by the following convolution N(S) = Σ_ssminN(s)^s_min-1N(S-s). In a forthcoming article we will show how the Moretto charge correlation can be calculated explicitly in the frame of the minimal information model. More generally these formulae are useful in domains where the fragment classes (infinite fragments, evaporation residues, light particles, intermediate mass fragments, liquid and gaseous phases... ) are defined with respect to their sizes. This article introduces recursive relations allowing the calculation of the number of partitions with constraints on the minimum and/or on the maximum fragment size. (author)