Dimension of RC-lattices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909779933265920 |
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| author | Bhavale, Ashok Nivrutti |
| author_facet | Bhavale, Ashok Nivrutti |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension of RC-lattices Bhavale, Ashok Nivrutti Combinatorics 06A05, 06A06, 06A07 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. |
| title | Dimension of RC-lattices |
| topic | Combinatorics 06A05, 06A06, 06A07 |
| url | https://arxiv.org/abs/2501.08318 |