Suppose we have two permutations x and y, represented as rank vectors. The Hamming distance between them is the number of entries in the two vectors which disagree. The Cayley distance is the minimum number of transpositions necessary to map x to y. See <http://www.liga.ens.fr/~deza/papers/voldpapers/huang/huangperm.pdf> for more information if needed. Let H(x, y) denote the Hamming distance, and C(x, y) denote Cayley distance


It appears the following holds: For every x, y, we have C(x, y) <= H(x, y) <= 2 \* C(x, y).


I'm looking for a citation for the above relationship. Thanks!



Hamming distance approximates Cayley distance on permutations: citation wanted
This fact is stated in <http://arxiv.org/abs/1202.0932v1>


