Talk:The Erdős discrepancy problem

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(quasi-multiplicative sequence)
 
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Every <math>\pm 1</math> sequence is on this form. E.g. take G to be the positive rationals with multiplication and let the function be the inclusion function. Do you mean "to a finite Abelian group G"? --[[User:SuneJ|SuneJ]] 11:29, 9 January 2010 (UTC)
Every <math>\pm 1</math> sequence is on this form. E.g. take G to be the positive rationals with multiplication and let the function be the inclusion function. Do you mean "to a finite Abelian group G"? --[[User:SuneJ|SuneJ]] 11:29, 9 January 2010 (UTC)
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Obviously, taking G=C2 yields the usual multiplicative sequence, but what about C4? What is the longest sequence with discrepancy 2 using G=C4?

Current revision

Terminology for zero-based APs

Could we abbreviate 'zero-based arithmetic progression' to ZAP (the 'H' for 'homogeneous' being redundant)? We'd then need a term for the discrepancy with respect to ZAPs, such as Z-discrepancy, unless it's clear from the context.

Repository of examples

We could do with a place on this Wiki to post interesting examples of sequences, and perhaps other experimental data, since currently they're scattered around the blog and I have one or two I'd like to add. In particular a page of 'longest sequences found so far' for various constraints and dimensions would be nice.

--Alec 09:01, 9 January 2010 (UTC)


You could place it in Experimental results. It would be great if we could use the wiki to post more information than we can on the blog. E.g: Short description of the program used to find the example, the program/code itself, status of the program (are we trying to find longer sequences with this program, or why not) and author of the program. Perhaps we could also create wish list: A page that only contains the short description of programs that have not been written. --SuneJ 09:18, 9 January 2010 (UTC)

quasi-multiplicative sequence

"Let us also call a \pm 1 sequence quasi-multiplicative if it is a composition of a completely multiplicative function from \mathbb{N} to an Abelian group G with a function from G to {-1,1}."

Every \pm 1 sequence is on this form. E.g. take G to be the positive rationals with multiplication and let the function be the inclusion function. Do you mean "to a finite Abelian group G"? --SuneJ 11:29, 9 January 2010 (UTC) Obviously, taking G=C2 yields the usual multiplicative sequence, but what about C4? What is the longest sequence with discrepancy 2 using G=C4?

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