Year: 2026
Type: preprint
Abstract: The cubic pancake graphs are Cayley graphs over the symmetric group Sn generated by three prefix reversals. There is the folllowing open problem: characterize all the sets of three prefix reversals that generate Sn. Blanco and Golubyatnikov give a complete solution of the problem when any of the two smallest or the two largest lengths but n are included in a triple of prefix reversals. According to their conjectures, we give some conditions implying a triple of prefix reversals does not generate Sn. Moreover, Using the symmetric groups that can already be generated by three prefix reversals, we can derive some recurrence conditions.
Source: arXiv (Cornell University)
Authors: Lei, Yexiao, Zhao, Jinxing, Zhu, Ziyu, Wu, Yang
Institution: Inner Mongolia University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2433029775
OpenAlex ID: W7223414684