Vol. 11, No. 3, 2018

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
Abstract

We define a collection of functions si 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 si-local moves, and proves that si-local moves correspond to the maps si acting on standard Young tableaux. We also prove that the graph of si-local moves is a connected, graded poset with unique minimal and maximal elements. We then extend this discussion to functions siC that mimic reflections in the Weyl group of type C. 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
Mathematical Subject Classification 2010
Primary: 92E10, 05A05, 05C40
Milestones
Received: 30 October 2014
Revised: 9 June 2017
Accepted: 17 July 2017
Published: 20 October 2017

Communicated by Ann N. Trenk
Authors
Laura Del Duca
Department of Mathematics and Statistics
Smith College
Northampton, MA
United States
Jennifer Tripp
Department of Mathematics and Statistics
Smith College
Northampton, MA
United States
Julianna Tymoczko
Department of Mathematics and Statistics
Smith College
Northampton, MA
United States
Judy Wang
Department of Mathematics and Statistics
Smith College
Northampton, MA
United States