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Sidon set

Defines: 
$B_h[g]$ set
Keywords: 
difference set
Synonym: 
Sidon sequence
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

11B05 no label found11B34 no label found

Comments

If we can stop talking about elliptical spaces in hypothetically large n-dimensional space and curvature tensors of antitime for a minute, I would like to ask a very mundane, perhaps even vulgar, question, and I will be grateful to anyone who doesn't mind to step down from the usual lofty planes to such a low level of inquiry for a minute.

Why does the Mian-Chowla sequence go 1, 2, 4, 8, 13, 21, 31, ... (A5282)? Why couldn't it go, say, 1, 2, 3, ... ? To rule out 3 the only thing I can come up with is making the sequence 0, 1, 2, 4, ... but then I still can't rule out 7 to favor 8. Have I missed something very basic here?

Isn't is just because you would than have 1+3=2+2=4, so those two sums of sequence entries wouldn't be distinct?

Cam

For those of us not in th know, would someone be so kind as to define the Mian-Chowla sequence? Preferrably, make this definition an entry for the benefit of the beknighted and bewildered of future generations.

The definition that is repeated by many sources roughly goes like this:

a_1 = 1. For n > 1, using the greedy algorithm, choose for a_n the smallest integer such that each a_i + a_j for 0 < i <= n and 0 < j <= n is unique (the pairwise sums).

Some definitions also specify that i = j is not considered, others add that maybe i = j is allowed when also i = j = n.

From what I can tell, the original definition is in a paper in an Indian journal, but since I can't read Indian, I don't even dare look up that paper.

As a woman, and uninterested in knowledge encryption as so many men are, I can admit that I don't understand exactly how the greedy algorithm fits into this. I understand how it applies to making change given a set of coin or bill currency, but I'm not sure how it works here.

At the very least I have to applaud PrimeFan's courage in admitting to not understanding something. Such an admission doesn't make you any less of a man.

I certainly don't mean to encrypt any knowledge. CompositeFan has pretty much correctly recapitulated what is most often repeated about the Mian-Chowla sequence.

But her incorrect remark about the "Indian language" (of which there are many) leads me to believe that the journal in question might be in English after all.

As for gender politics, I don't care to comment on that.

Isn't is just because you would than have 1+3=2+2=4, so those two sums of sequence entries wouldn't be distinct?

Cam

That would be true if i = j is acceptable as a pairwise sum. I'm hoping the original journal paper is in English and explains this in a little more detail.

It has to be. Otherwise you spin your wheels in the dirt for like, forever. The i != j in the Guy book is a mistake.

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