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RNA, local
moves on plane trees, and transpositions on tableaux
Laura Del Duca, Jennifer Tripp, Julianna Tymoczko and Judy Wang
Vol. 11 (2018), No. 3, 383–411
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Abstract |
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We define a collection of functions on the set of plane trees (or standard Young tableaux). The functions are adapted from transpositions in the representation theory of the symmetric group and almost form a group action. They were motivated by local moves in combinatorial biology, which are maps that represent a certain unfolding and refolding of RNA strands. One main result of this study identifies a subset of local moves that we call -local moves, and proves that -local moves correspond to the maps acting on standard Young tableaux. We also prove that the graph of -local moves is a connected, graded poset with unique minimal and maximal elements. We then extend this discussion to functions that mimic reflections in the Weyl group of type . The corresponding graph is no longer connected, but we prove it has two connected components, one of symmetric plane trees and the other of asymmetric plane trees. We give open questions and possible biological interpretations. |
Keywords
plane trees, RNA, Young tableaux, connected components,
permutation
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Mathematical Subject Classification 2010
Primary: 92E10, 05A05, 05C40
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Milestones
Received: 30 October 2014
Revised: 9 June 2017
Accepted: 17 July 2017
Published: 20 October 2017
Communicated by Ann N. Trenk
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Authors |
| Laura Del Duca | |
| Department of Mathematics and
Statistics Smith College Northampton, MA United States |
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| Jennifer Tripp | |
| Department of Mathematics and
Statistics Smith College Northampton, MA United States |
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| Julianna Tymoczko | |
| Department of Mathematics and
Statistics Smith College Northampton, MA United States |
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| Judy Wang | |
| Department of Mathematics and
Statistics Smith College Northampton, MA United States |
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