A note on antichains of words

Abstract

We can compress the word 'banana' as $xyyz$, where $x =$ 'b', $y = $ 'an',$z = $ 'a'. We say that 'banana' encounters $yy$. Thus a 'coded' version of $yy$ shows up in 'banana'. The relation '$u$ encounters $w$' is transitive, and thus generates an order on words. We study antichains under this order. In particular we show that in this order there is an infinite antichain of binary words avoiding overlaps.