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arXiv · 2501.08318

Dimension of RC-lattices

Ashok Nivrutti Bhavale
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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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Ashok Nivrutti Bhavale. 2025-09-10. Dimension of RC-lattices. https://arxiv.org/abs/2501.08318

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