Papers › RNA, local moves on plane trees, and transpositions on tableaux
RNA, local moves on plane trees, and transpositions on tableaux
Laura Seegerer, Jennifer Tripp, Julianna Tymoczko, Judy Wang
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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 sᵢ^C 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 and the other of asymmetric plane trees. We give open questions and possible biological interpretations.
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