Folding Words Around Trees: Models Inspired by RNA
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At the intersection of mathematics and biology, we find mathematical models built to address biological questions as well as new mathematical theories inspired by biological structures. In this chapter, we explore a combinatorial model for folding words around plane trees which is inspired by the bonds that form between nucleotides in a single-stranded RNA molecule. This chapter walks the reader through the construction of valid plane trees, structures formed by folding a word in a complementary alphabet around a plane tree, and enumerates the class of words with exactly one such folding. Valid plane trees are relatively unexplored combinatorial objects, and while we present several potential research projects, a careful reader can come up with many additional directions for further study.
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