CODEWITHSUNDEEP
algorithmmathpermutation
thinkhy
thinkhy

Reputation: 933

Is "Cantor expansion" applied in any computer technologies?

The Cantor expansion of the natural number n is

 n = ak * k!+a(k − 1) *(k −1)!+.... + a2 * 2!+a1 *1!

where all the ai (digits) satisfy 0 ≤ ai ≤ i

I knew it can be used to generate full-permutation, even some questions about it comes up in interviews, but I hasn't yet seen where it's applied in computer technologies. Anyone has any clue on this?

Upvotes: 0

Views: 302

Answers (1)

thinkhy
thinkhy

Reputation: 933

Searching with keyword "cantor expansion" in Google Patent, I found an example which used cantor expansion to encode info.

...... the recipient will extract an arrangement which g a head keywords: H '1; H' 2, ..., H 'g. Next, we can further expansion by Cantor:

[0034] k = a [l] * (g_l)! + A [2] * (g_2)! + ... + A [g] * 0! + L

[0035] The calculation of the arrangement is that the partial ordering of the k-th order, then the HTTP request is encoded n_segk fragments. Wherein, a [u] represents the arrangement satisfies H '' number H' j of u's. Then the packet format HTTP Ci requests sent to fixedly hold the partial order of the i-th order, so as to achieve the purpose of transferring data distributed fragmentation. Such analytical methods can hide and maintain maximum independence and encoding and retrieval accuracy. Wherein, l <= i, j, u, k <= 2n.

Upvotes: 1

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