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.
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Communicated by I. Rival
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Elbaz, J. Substitution and atomic extension on greedy posets. Order 3, 235–244 (1986). https://doi.org/10.1007/BF00400287
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DOI: https://doi.org/10.1007/BF00400287