Let $\pi = (a_{1}, a_{2},\ldots,a_{s})$ be an (integral) partition of the integer $n = a_{1} + \cdots + a_{s}$. One calls subsum of $\pi $ every sum $ a_{{i}_{l}} +\cdots + a_{{i}_{t}}\ (i_{l} < \cdots < i_{t})$. Let $\Sigma (\pi ) \subset [0,n]$ be the set of all subsums of $\pi $. The paper is concerned with $\Sigma (\pi )$, which is far from being an arbitrary subset of $[n,0]$. One studies the 2 first “connected components” of $\Sigma (\pi )$, the partitions for which $\Sigma (\pi )$ has 1, 2, or 3 connected components, and the partitions for which the complement of $\Sigma (\pi )$ in $[n,0]$ is not too big. On the other hand, let $Q$ be a fixed finite set of positive integeers ; let $p(n;Q)$ be the number of partitions $\pi $ of $n$ such that $Q \cap \Sigma (\pi ) = \emptyset $ (so that $p(n;\emptyset )$ is the number ically denoted by $p(n)$) ; one studies the asymptotic behaviour of $p(n;Q)$ as $n \rightarrow \infty $ ; for instance, if a is an integer, one has $p (n; \{a\})/p(n) \sim (\pi / \sqrt {6})^{[a/2] + 1} u(a)/n^{([a/2] +1)/2}$ as $n \rightarrow \infty $, where $u(a)$ is an integer such that log $u(a) \sim (a/2)$ log $a$ as $a \rightarrow \infty $. One shows that, when $n$ is big, almost all partitions $\pi $ of $n$ such that $\Sigma (\pi ) \cap \{1, 2, \ldots, a\} = \emptyset $ verify $\Sigma (\pi ) = \{a + 1, a + 2, a + 3, \ldots, n-a-1\}$.