Generalized Goulden-Yong duals and signed minimal factorizations

Abstract

We show the equivalence between one-way reflections and relative projective representations. We construct generalized Goulden-Yong duals using reverse Garside element actions and folded chord diagrams. We give two applications of the generalized Goulden-Yong duals: constructing generalized Prüfer codes and counting signed factorizations using the matrix-tree theorem.

33 pages, 15 figures. v2: updated type D Prüfer codes following a suggestion by Olivier Bernardi and made some minor changes