Substitution and atomic extension on greedy posets |
| |
Authors: | Jonathan Elbaz |
| |
Institution: | (1) Département Informatique Appliquée, Ecole des Mines, 158, Cours Fauriel, 42023 Saint-Etienne Cédex 2, France |
| |
Abstract: | In this paper, we study the operations of substitution and atomic extension on greedy posets. For the substitution operation, if P=(P
1
, x, P
2
)is a greedy poset, then P
1
and P
2
are greedy posets, the converse being false. However, for the atomic extension, P=P
1
(x, P
2
)is a greedy poset if and only if P
1
and P
2
are greedy posets. We prove also that the class of greedy semi-partitive lattices is the smallest one containing M
n
(n 2), B
3
and closed by atomic extension. The class C
n
of greedy posets with jump number n is infinite. However, we show that C
n
can be obtained, in a very simple way, from a subclass D
n
of finite cardinal ity. We construct D
n
for n=1, 2. |
| |
Keywords: | Primary 06A10 secondary 06A05 |
本文献已被 SpringerLink 等数据库收录! |
|