  In this paper, we present, for any integer d, a description of the set of
hooks in a d-symbol. We then introduce generalized hook length functions for a
d-symbol, and prove a general result about them, involving the core and
quotient of the symbol. We list some applications, for example to the
well-known hook lengths in integer partitions. This leads in particular to a
generalization of a relative hook formula for the degree of characters of the
symmetric group discovered by G. Malle and G. Navarro in [3].
