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In the following paper http://www.math.ucsd.edu/~ronspubs/74_01_van_der_waerden.pdf, just in the first paragraph the author defines what $l$-equivalence for two m-tuples $\in [0,l]^m$ means. Can somebody please give me a more precise definition of what he means? I am not even sure what $[0,l]^m$ stands for, although I expect its just $\{0,1,\dots,l\}^m$.

Thanks

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    I think it just means that (a,b,x) and (a,b,y) are 2-equivalent. I'vve not been able to understand the proof yet.2012-11-27

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