Geodesic
Ordering the Representations of ${{S}_{n}}$ Using the Interchange Process
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 13-30

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DOI

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.
DOI : 10.4153/CMB-2011-147-2
Mots-clés : 82C22, 60B15, 43A65, 20B30, 60J27, 60K35, Aldous' conjecture, interchange process, symmetric group, representations 
Alon, Gil; Kozma, Gady. Ordering the Representations of ${{S}_{n}}$ Using the Interchange Process. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 13-30. doi: 10.4153/CMB-2011-147-2
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