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• W2200654564 abstract "In Card shuffling and the decomposition of tensor products, Jason Fulman explores a Markov chain on partition diagrams, where each step removes a box then adds a new box. The stationary distribution of this chain is the Plancherel measure, which suggests that it is the image under the RSK-shape map of a chain on permutations with uniform stationary distribution. Fulman proves that one possible lift, starting from the identity permutation, is the shuffle: remove the top card of a deck, and reinsert it at a uniformly chosen position. We construct a different lift, valid from more initial distributions, using a new and very general result regarding Markov chains from non-negative linear maps. This abstract result essentially reduces the lift construction to a well-known fact: the algebra of symmetric functions is a subquotient of the Malvenuto-Reutenauer Hopf algebra of permutations. The multistep transition probabilities of this new lift chain, starting from the identity permutation, agree with those of the top-to-random chain." @default.
• W2200654564 created "2016-06-24" @default.
• W2200654564 creator A5050670196 @default.
• W2200654564 date "2015-08-06" @default.
• W2200654564 modified "2023-09-27" @default.
• W2200654564 title "A Hopf-Algebraic Lift of the Down-Up Markov Chain on Partitions to Permutations" @default.
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