Van Der Waerden Theorem

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
0% accept rate - are you familiar with the concept of accepting answers to your questions? Please see what the site documentation says about it. –  Gerry Myerson Mar 23 '12 at 0:44
@Gerry: How about "Dear Sir, would you please take a look at this discussion on accepting answers and consider accepting answers to a few of your problems?" –  The Chaz 2.0 Mar 23 '12 at 1:11
$(x_1,\cdots,x_m)$ 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 $i=j+1,\cdots ,m$.