2024/12/04 by B. P. Aware, Aware, B. P., A. N. Bhavale +1
Computer Science · #06A06 #06A07 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2412.03627
openalex publication_date 2024/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2020 Bhavale and Waphare introduced the concept of a nullity of a poset as nullity of its cover graph. According to Bhavale and Waphare, if a dismantlable lattice of nullity k contains r reducible elements then 2 ≤ r ≤ 2k. In 2003 Pawar and Waphare counted all non-isomorphic lattices with equal number of elements and edges, which are precisely the lattices of nullity one. Recently, Bhavale and Aware counted all non-isomorphic lattices on n elements having nullity up to two. Bhavale and Aware also counted all non-isomorphic lattices on n elements, containing up to three reducible elements, having 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.