Generalized Goulden-Yong duals and signed minimal factorizations
Combinatorics
2024-04-24 v2 Representation Theory
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 Pr\"{u}fer codes and counting signed factorizations using the matrix-tree theorem.
Keywords
Cite
@article{arxiv.2311.05732,
title = {Generalized Goulden-Yong duals and signed minimal factorizations},
author = {Shujian Chen and Kiyoshi Igusa},
journal= {arXiv preprint arXiv:2311.05732},
year = {2024}
}
Comments
33 pages, 15 figures. v2: updated type D Pr\"{u}fer codes following a suggestion by Olivier Bernardi and made some minor changes