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arXiv · 1302.2310

Two Propositions Involving the Standard Representation of $S_n$

Shanshan Ding
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Abstract

We present here two standalone results from a forthcoming work on the analysis of Markov chains using the representation theory of $S_n$. First, we give explicit formulas for the decompositions of tensor powers of the defining and standard representations of $S_n$. Secondly, we prove that any Markov chain on $S_n$ starting with one fixed point and whose increment distributions are class measures will always average exactly one fixed point.

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Shanshan Ding. 2013-02-10. Two Propositions Involving the Standard Representation of $S_n$. https://arxiv.org/abs/1302.2310

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