Dimension of RC-lattices

2025/01/14 by Bhavale, Ashok Nivrutti
#06A05 #06A06 #06A07 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.08318

Abstract

In 1941 Dushnik and Miller introduced the concept of dimension of a poset. In 2020 Bhavale and Waphare introduced the concept of an RC-lattice as a lattice in which all the reducible elements are lying on a chain. In this paper, we obtain the dimension of adjunct sum of two lattices. We obtain a bound on the dimension of a dismantlable lattice in terms of its nullity. We also prove that the dimension of an RC-lattice on n elements is at the most three. Consequently, we prove that an RC-lattice is non planar if and only if its dimension is three.

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