We define a collection of functions $s_i$ on the set of plane trees (orstandard Young tableaux). The functions are adapted from transpositions in therepresentation theory of the symmetric group and almost form a group action.They were motivated by $\textit{local moves}$ in combinatorial biology, whichare maps that represent a certain unfolding and refolding of RNA strands. Onemain result of this study identifies a subset of local moves that we call$s_i$-local moves, and proves that $s_i$-local moves correspond to the maps$s_i$ acting on standard Young tableaux. We also prove that the graph of$s_i$-local moves is a connected, graded poset with unique minimal and maximalelements. We then extend this discussion to functions $s_i^C$ that mimicreflections in the Weyl group of type $C$. The corresponding graph is no longerconnected, but we prove it has two connected components, one of symmetric andthe other of asymmetric plane trees. We give open questions and possiblebiological interpretations.
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