equidistributed

Two statistics $σ, μ$ are equidistributed ( $σ \sim μ$ ) if

# {w \in S_{n} ∣ σ (w) = k} = # {w \in S_{n} ∣ μ (w) = k}

for all $k$ .

This forms an equivalence relation on statistics on $S_{n}$ .

Examples