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arXiv · 0709.1477

Random walks on quasisymmetric functions

Patricia Hersh·Samuel K. Hsiao
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Abstract

Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations. Spectral results are also obtained. Several well-studied random walks are now realized this way: Stanley's QS-distribution results from endomorphisms given by evaluation maps, a-shuffles result from the a-th convolution power of the universal character, and the Tchebyshev operator of the second kind introduced recently by Ehrenborg and Readdy yields traditional riffle shuffles. A conjecture of Ehrenborg regarding the spectra for a family of random walks on ab-words is proven. A theorem of Stembridge from the theory of enriched P-partitions is also recovered as a special case.

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Patricia Hersh, Samuel K. Hsiao. 2007-09-10. Random walks on quasisymmetric functions. https://arxiv.org/abs/0709.1477

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