“…For the inversion vector representation of permutation, a simple component-wise scalar quantization achieves the optimal rate distortion trade-off, as shown in [3]. In particular, given D = cn 1+δ , 0 < δ < 1, for the (k − 1)-th component of the inversion vector (k = 2, · · · , n), we quantize k points in [0 : k − 1] uniformly with m k = kn/(2D) points, resulting component-wise average distortion D k = D/n and overall average distortion = n k=2 D k ≤ D, and log of codebook size log M n = n k=2 log m k = n k=2 log kn/(2D) = (1 − δ)n log n − O (n) .…”