Dugger, DanielPhillips, Bo2024-01-092024-01-092024-01-09https://hdl.handle.net/1794/29184In this paper, we build on the work of Lipshitz, Ozsv\'{a}th, and Thurston by constructing an algorithm that generates a weighted $A_\infty$-diagonal given a family of contractions of the weighted associahedron complexes. Using this, we exhibit a new weighted $A_\infty$-diagonal and relate it to the unweighted $A_\infty$-diagonal exhibited by Masuda-Thomas-Tonks-Vallete given by so-called ``right-moving trees.''en-USAll Rights Reserved.a-infinityalgebrahomotopyElectronic Thesis or Dissertation