  The Macdonald symmetric functions are used to define measures on the set of
all partitions of all integers. Probabilistic algorithms are given for growing
partitions according to these measures. The case of Hall-Littlewood polynomials
is related to the finite classical groups, and the corresponding algorithms
simplify. The case of Schur functions leads to a $q$-analog of Plancharel
measure, and a conditioned version of the corresponding algorithms yields
generalizations of the hook walk of combinatorics.
