Abstract
This paper deals with sufficient conditions on a poset in order to get it spectral. A motivating question is the following (p. 833 [LO76]): "If X is a height 1 poset such that for all x ≠ y ∈X, ↑ x ∩ ↑y and ↓ x ∩ ↓y are finite, is X spectral?" We obtain the some sufficient conditions for such a poset X to be spectral. In particular, we prove that either if there is a finite subset F ⊆X such that ↓ F ⊇Min X, or if diam X ≤ 2, then the poset X is spectral.
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