A \(q\)-analog of the hook walk algorithm for random Young tableaux (Q1310601)

The \(q\)-hook walk, a probabilistic algorithm, is defined. Its special case with \(q=1\) has been used in literature to obtain the number \(f_ \lambda\) of Young tableaux of a given shape \(\lambda\), and to find a procedure for efficient simulation of random Young tableaux with probabilities \(P_ \lambda={f_ \lambda\over |\lambda|!}\) depending only on their shape \(\lambda\). The author has presented in this paper an extension and generalization of these results.