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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) + 1 <= H(x, y) <= 2 * C(x, y).

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

2 added 4 characters in body

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) + 1 <= H(x, y) <= 2 * C(x, y).

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

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# Hamming distance approximates Cayley distance on permutations: citation wanted

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!