Counting of lattices containing up to four comparable reducible elements and having nullity up to three
Abstract
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.
Cite
@article{arxiv.2412.03627,
title = {Counting of lattices containing up to four comparable reducible elements and having nullity up to three},
author = {B. P. Aware and A. N. Bhavale},
journal= {arXiv preprint arXiv:2412.03627},
year = {2025}
}
Comments
Correction in Lemma 1.3(statement and proof), Lemma 1.5(statement and proof), and Proposition 3.3(only ststement). Rest of the file is same as v1