N-free extensions of posets.Note on a theorem of P.A.Grillet

Maurice Pouzet, Nejib Zaguia

Let $S\_N(P)$ be the poset obtained by adding a dummy vertex on each diagonal edge of the $N$'s of a finite poset $P$. We show that $S\_N(S\_N(P))$ is $N$-free. It follows th…