Abstract. A new type of dependencies in a relational database model is investigated. If $b$ is an attribute, $A$ is a set of attributes then it is said that $b(p,q)$-depends on $A$, in notation $A\mathop{\longrightarrow}^{(p,q)}b$, in a database $r$ if there are no $q+1$ relations in $r$ such that they have at most $p$ different values in $A$, but $q+1$ different values in $b$. $(1,1)$-dependency is the classical functional dependency. Let ${\bf J}(A)$ denote the set $\{b:A\mathop{\longrightarrow}^{(p,q)}b\}$. Using some characterization of the set function ${\bf J}(A)$ we give estimates for the minimum number of records in a database system that results the set functions ${\bf J}(A)$.

AMS Subject Classification (1991): 68P15, 68R05, 05D05

Received October 19, 1994, and in revised form April 5, 1995. (Registered under 5628/2009.)