Ewan Cassidy

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math.RT2025

Random permutations acting on $k$ --tuples have near--optimal spectral gap for $k = poly (n)$

Ewan Cassidy

We extend Friedman's theorem to show that, for any fixed $r > 1$ , a random $2 r$ --regular Schreier graph associated with the action of $r$ uniformly random permutations of $[n]$ on $k…

math.RT2025

Projection formulas and a refinement of Schur--Weyl--Jones duality for symmetric groups

Ewan Cassidy

Schur--Weyl--Jones duality establishes the connection between the commuting actions of the symmetric group $S_{n}$ and the partition algebra $P_{k} (n)$ on the tensor space $\left(\…

Random permutations acting on k--tuples have near--optimal spectral gap for k=poly(n)

Projection formulas and a refinement of Schur--Weyl--Jones duality for symmetric groups

Random permutations acting on $k$ --tuples have near--optimal spectral gap for $k = poly (n)$