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Folding Words Around Trees: Models Inspired by RNA

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Part of the Foundations for Undergraduate Research in Mathematics book series (FURM)

Abstract

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Haverford CollegeHaverfordUSA
  2. 2.Davidson CollegeDavidsonUSA

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