Counting of lattices containing up to four comparable reducible elements and having nullity up to three

In 1940, Birkhoff raised the open problem of computing of all posets/lattices on \(n\) elements up to isomorphism for small \(n\). Many authors tried to solve this problem by providing algorithms such as nauty. In 2020, Gebhardt and Tawn given an orderly algorithm for constructing unlabelled lattices of given size and explicitly obtained the number of lattices on up to \(20\) elements. In 2020, Bhavale and Waphare introduced the concept of nullity of a poset as the nullity of its cover graph. Recently, Bhavale and Aware counted lattices having nullity up to two. Bhavale and Aware also counted all non-isomorphic lattices on \(n\) elements, containing up to three reducible elements, having arbitrary nullity \(k ≥ 2\). In this paper, we count up to isomorphism the class of all lattices on \(n\) elements containing four comparable reducible elements, and having nullity three.