论文部分内容阅读
The problems we consider in this talk arose in a probabilistic treatment of card shuffling. However we treat them as stochastic discrete time switching systems. When a deck of n cards is used the state space has n! elements so that for even small n the problem becomes intractable. We show that we can reduce the dimension of the state space first to the number of partitions of n into non-negative integer parts and then using this we reduce the state space to size n for the transposition shuffle. We demonstrate the procedure in this talk with decks of size 6 and 20.We define a large set of permutations and our goal in the shuffle is to hit this set. Using standard stochastic process theory we make this.