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Can someone explain me what's the meaning of the term "l-equivalent" in the following paper:

http://www.math.ucsd.edu/~ronspubs/74_01_van_der_waerden.pdf

?

I saw the definition at the first lines, but couldn't understand what is its meaning.

Hope someone will be able to help me

Thanks !

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Please make the question self contained. –  Beni Bogosel Mar 22 '12 at 19:18

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$(x_1,\cdots,x_m)$ and $(x_1,\cdots,x_m)$ are called $l$-equivalent if either $x_i,y_i<l$ for $i=1,\cdots ,m$ or if for some $j\leq m$ we have $x_j=y_j=l$ and $x_i,y_i<l$ for $i=j+1,\cdots ,m$.

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Thanks a lot!!!!!!!!!!!!!!!!!!!!!!!!! –  joshua Mar 23 '12 at 7:57

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