Explorations of the Aldous Order on Representations of the Symmetric Group

The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. Howeve...

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Main Author:	Newhouse, Jack
Format:	Others
Published:	Scholarship @ Claremont 2012
Subjects:	20C30 Representations of Finite Symmetric Groups 05E10 Combinatorial Aspects of Representation Theory 60J27 Continuous-time Markov Processes on Discrete State Spaces 20B30 Symmetric Groups
Online Access:	https://scholarship.claremont.edu/hmc_theses/35 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1034&context=hmc_theses

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spelling	ndltd-CLAREMONT-oai-scholarship.claremont.edu-hmc_theses-10342019-10-16T03:06:13Z Explorations of the Aldous Order on Representations of the Symmetric Group Newhouse, Jack The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements. 2012-05-31T07:00:00Z text application/pdf https://scholarship.claremont.edu/hmc_theses/35 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1034&context=hmc_theses © Jack Newhouse default HMC Senior Theses Scholarship @ Claremont 20C30 Representations of Finite Symmetric Groups 05E10 Combinatorial Aspects of Representation Theory 60J27 Continuous-time Markov Processes on Discrete State Spaces 20B30 Symmetric Groups
collection	NDLTD
format	Others
sources	NDLTD
topic	20C30 Representations of Finite Symmetric Groups 05E10 Combinatorial Aspects of Representation Theory 60J27 Continuous-time Markov Processes on Discrete State Spaces 20B30 Symmetric Groups
spellingShingle	20C30 Representations of Finite Symmetric Groups 05E10 Combinatorial Aspects of Representation Theory 60J27 Continuous-time Markov Processes on Discrete State Spaces 20B30 Symmetric Groups Newhouse, Jack Explorations of the Aldous Order on Representations of the Symmetric Group
description	The Aldous order is an ordering of representations of the symmetric group motivated by the Aldous Conjecture, a conjecture about random processes proved in 2009. In general, the Aldous order is very difficult to compute, and the proper relations have yet to be determined even for small cases. However, by restricting the problem down to Young-Jucys-Murphy elements, the problem becomes explicitly combinatorial. This approach has led to many novel insights, whose proofs are simple and elegant. However, there remain many open questions related to the Aldous Order, both in general and for the Young-Jucys-Murphy elements.
author	Newhouse, Jack
author_facet	Newhouse, Jack
author_sort	Newhouse, Jack
title	Explorations of the Aldous Order on Representations of the Symmetric Group
title_short	Explorations of the Aldous Order on Representations of the Symmetric Group
title_full	Explorations of the Aldous Order on Representations of the Symmetric Group
title_fullStr	Explorations of the Aldous Order on Representations of the Symmetric Group
title_full_unstemmed	Explorations of the Aldous Order on Representations of the Symmetric Group
title_sort	explorations of the aldous order on representations of the symmetric group
publisher	Scholarship @ Claremont
publishDate	2012
url	https://scholarship.claremont.edu/hmc_theses/35 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1034&context=hmc_theses
work_keys_str_mv	AT newhousejack explorationsofthealdousorderonrepresentationsofthesymmetricgroup
_version_	1719268820869185536

Explorations of the Aldous Order on Representations of the Symmetric Group

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