On modular pairs in posets

Abstract

In this paper, we have introduced a new concept of a modular pair in terms of maximal elements of lower cone (L) and minimal elements of upper cone (U) in posets. The relation between our definition and the existing definitions of modular pairs in posets has been studied for different classes of posets. We succeeded in characterizing a modular pair by means of forbidden configuration in general posets. We have obtained several characterizations of modular pairs in atomistic and semi-orthogonal posets. We have also introduced ∇-relation in posets.