Aldous property for full-flag Johnson graphs
Gary Greaves, Haoran Zhu
TL;DR
This paper proves that full-flag Johnson graphs exhibit an Aldous-type spectral-gap phenomenon, confirming two conjectures and linking their spectral properties to a specific Schreier quotient.
Contribution
It establishes that the spectral gap of full-flag Johnson graphs equals that of a related Schreier quotient, confirming conjectures about their spectral properties.
Findings
Spectral gap of full-flag Johnson graph equals that of its Schreier quotient
Confirmation of two conjectures related to spectral gaps
Supports Aldous-type spectral-gap phenomena in these graphs
Abstract
We show that the full-flag Johnson graph has spectral gap equal to that of its Schreier quotient arising from the point-stabiliser equitable partition. Our results confirm two conjectures posed by Huang, Huang, and Cioab\u{a}, which imply an Aldous-type spectral-gap phenomenon for full-flag Johnson graphs.
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Taxonomy
TopicsGraph theory and applications · Finite Group Theory Research · Limits and Structures in Graph Theory