English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Aldous' spectral gap conjecture states that the second largest eigenvalue ofany connected Cayley graph on the symmetric group Sn with respect to a set oftranspositions is achieved by the standard representation of Sn. Thiscelebrated conjecture, which was proved in its general form in 2010, hasinspired much interest in searching for other families of Cayley graphs on Snwith the property that the largest eigenvalue strictly smaller than the degreeis attained by the standard representation of Sn. In this paper, we prove threeresults on normal Cayley graphs on Sn possessing this property for sufficientlylarge n, one of which can be viewed as a generalization of the "normal" case ofAldous' spectral gap conjecture.

Aldous' spectral gap property for normal Cayley graphs on symmetric groups