# LOWER BOUNDS OF THE NUMBER OF JUMP OPTIMAL LINEAR EXTENSIONS : PRODUCTS OF SOME POSETS

• Jung, Hyung-Chan (Liberal Arts and Sciences, Korea Institute of Technology and Education, Gajeon-Ri, Gyungchon, Chonan, Chungnam, 333-860)
• Published : 1995.08.01

#### Abstract

Let P be a finite poset and let $\mid$P$\mid$ be the number of vertices in pp. A subposet of P is a subset of P with the induced order. A chain C in P is a subposet of P which is a linear order. The length of the chain C is $\mid$C$\mid$ - 1. A linear extension of a poset P is a linear order $L = x_1, x_2, \ldots, x_n$ of the elements of P such that $x_i < x_j$ is P implies i < j. Let L(P) be the set of all linear extensions of pp. E. Szpilrajn [5] showed that L(P) is not empty.