Talk:Sidon sequence

I don't understand why the "proof" that Golomb rulers and finite Sidon sequences are obtainable from each other works.

Is there something wrong with this example which involves three terms rather than four?

Consider: 1, 4, 6, 8; pairs of marks yield 5, 7, 9, 10, 12, 14 but there are two equal differences: 6-4 = 2 and 8-6 =2. There are three indices i, j, and k here rather than 4 indices. So with the indices ordered i, j, k, if 2a(j) = a(k) + a(i) we can have equality. 2(6) = 4 + 8. So we have a finite Sidon sequence but not a golomb ruler.

Am I missing something?

Cheers,

Joseph Malkevitch

jmalkevitch@york.cuny.edu — Preceding unsigned comment added by Jmalkevitch (talk • contribs) 17:26, 23 December 2011 (UTC)

I think that you missed the "=" of the "≤" in the definition, that is, in computing the sums the possibility that i = j must be included. With this clarification, your example is seen to not be a Sidon sequence precisely because 6 + 6 = 4 + 8. Bill Cherowitzo (talk) 23:13, 13 January 2012 (UTC)

Error in parenthetical about approximate Sidon sets

In the parenthetical statement "(To be a Sidon sequence would require that c = 0.)" shouldn't that say c = 1? To be a Sidon sequence there should be at maximum one sum resulting in a given integer? Rodfreier (talk) 01:49, 24 February 2013 (UTC)

You're correct and I've fixed it. --JBL (talk) 02:39, 24 February 2013 (UTC)