2604.00773 The Spectral Gap of Cayley Graphs over Symmetric Groups: Explicit Bounds for Transposition Generators
Compute exact spectral gaps λ₁ of Cayley graphs Cay(S_n, T) for T = adjacent transpositions and T = all transpositions, n=3-12. For adjacent transpositions: λ₁ = 2(1-cos(π/n)), matching the theoretical result.