Marsh, RJ and Schroll, S (2013) A circular order on edge-coloured trees and RNA m-diagrams. Advances in Applied Mathematics, 54 (1). 11 - 26. ISSN 0196-8858
Abstract
We study a circular order on labelled, m-edge-coloured trees with k vertices, and show that the set of such trees with a fixed circular order is in bijection with the set of RNA m-diagrams of degree k, combinatorial objects which can be regarded as RNA secondary structures of a certain kind. We enumerate these sets and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m = 3, arises as an induction in the context of interval exchange transformations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013, Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Advances in Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Applied Mathematics, 54, 1, 2013, 10.1016/j.aam.2013.09.009 |
Keywords: | Tree; Edge-coloured; Labelled triangulation; Fuss–Catalan number; Enumeration; Tree of relations; RNA secondary structure; Polygon; m-Angulation; Induction; Interval exchange transformation; RNA m-diagram |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Jun 2014 11:39 |
Last Modified: | 22 Apr 2015 21:04 |
Published Version: | http://dx.doi.org/10.1016/j.aam.2013.09.009 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aam.2013.09.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79310 |