Kavli Affiliate: Zhuo Li
| First 5 Authors: Zhuo Li, Zhuo Li, , ,
| Summary:
We introduce a new group action on set systems, constructed as a semidirect
product of a permutation group and a group generated by twist and loop
complementation operations on a single element. This action extends the ribbon
group framework of Abrams and Ellis-Monaghan from ribbon graphs to set systems,
facilitating a systematic investigation of self-twuality. We prove that
different forms of self-twuality propagate through orbits under the group
action and establish a characterization of the orbit of a vf-safe delta-matroid
via multimatroids. As an application, we analyze orbits of ribbon-graphic
delta-matroids. Our work answers a question posed by Abrams and Ellis-Monaghan
and provides a unified algebraic framework for studying self-twuality in
combinatorial structures.
| Search Query: ArXiv Query: search_query=au:”Zhuo Li”&id_list=&start=0&max_results=3