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Ordering the Representations of
${{S}_{n}}$ Using the Interchange Process
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- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 1 / 01 March 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 13-30
- Print publication:
- 01 March 2013
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- Article
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Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett, and Richthammer, we define an associated order
$\prec $ on the irreducible representations of ${{S}_{n}}$. Aldous' conjecture is equivalent to certain representations being comparable in this order, and hence determining the “Aldous order” completely is a generalized question. We show a few additional entries for this order.
