Talk:Sattolo cycle: Difference between revisions
→Definition "each element ends up in a new position"
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: But, it's true also that it would be nice if there were some concise way of describing all possible results which wasn't the algorithm itself. (And, thanks for calling attention to that issue.) --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 02:04, 27 April 2020 (UTC)
:: <code>AB -> BA -> AB</code> is ''not'' a cycle; <code>BA</code> is. Similarly, <code>ABCD -> BADC -> ABCD</code> is not a cycle, but ''neither'' is <code>BADC</code>. If you don't believe me, you can read the first paragraph of the Wikipedia page on cyclic permutations (I won't bother linking it; I trust you can find it yourself). --[[User:Dick de Bill|Dick de Bill]] ([[User talk:Dick de Bill|talk]]) 14:
::: I think you should re-read [[wp:Cyclic_permutation|the wikipedia entry on cyclic permutations]] --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 19:44, 1 May 2020 (UTC)
:::: No Rdm, you should :) I see you're having trouble understanding that article, so let me quote the most relevant part for you:
::::: ''(...) given X = {1, 2, 3, 4}, the permutation (1, 3, 2, 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 (so S = X) is a 4-cycle, and the permutation (1, 3, 2) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 (so S = {1, 2, 3} and 4 is a fixed element) is a 3-cycle. '''On the other hand, the permutation that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}.'''''
:::: You will notice that you can replace the set X = {1, 2, 3, 4} with X' = {A, C, B, D} and the above stated still holds. Then you can re-read the last sentence of the quoted text (in bold for emphasis, to show how it relates to the example I gave which you're confused about):
::::: '''''On the other hand, the permutation that sends A to B, B to A, C to D and D to C is not a cyclic permutation because it separately permutes the pairs {A, B} and {C, D}.'''''
:::: I hope it's all clear now. If not, write me a personal message or something... [[User:Dick de Bill|Dick de Bill]] ([[User talk:Dick de Bill|talk]]) 21:10, 1 May 2020 (UTC)
:::::: Which is the part which states that showing a sequence of permuted states for a cycle does not or cannot represent that cycle? --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 23:02, 1 May 2020 (UTC)
::::::: Literally the first sentence of the article. It says "''a cyclic permutation (or '''cycle''') is a '''permutation of the elements'''''". Meaning: <code>BA</code> is the cycle, not <code>AB -> BA -> AB</code>. Anyways, this point is moot; my complaint which you didn't understand was that <code>BADC</code> is not a cycle, and I believe that has been clarified. I see no reason to take this discussion any further. --[[User:Dick de Bill|Dick de Bill]] ([[User talk:Dick de Bill|talk]]) 00:18, 2 May 2020 (UTC)
:::::::: BA is a cyclic permutation of AB, but it's not a cyclic permutation of BA. It's not usually necessary to emphasize this issue, but there are contexts where it can be important. Anyways, this has drifted away from the original point which is that there's a distinction between cycles and sattalo cycles, in the sense that some cycles are not sattalo cycles. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 01:05, 2 May 2020 (UTC)
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