The asymptotic number of planar, slim, semimodular lattice diagrams
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arXiv
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| Format: | Preprint |
| Published: |
2012
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| _version_ | 1866912097373257728 |
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| author | Czédli, Gábor |
| author_facet | Czédli, Gábor |
| contents | A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of these lattices of size n is asymptotically C times 2 to the n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1206_3679 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | The asymptotic number of planar, slim, semimodular lattice diagrams Czédli, Gábor Rings and Algebras 06C10 A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of these lattices of size n is asymptotically C times 2 to the n. |
| title | The asymptotic number of planar, slim, semimodular lattice diagrams |
| topic | Rings and Algebras 06C10 |
| url | https://arxiv.org/abs/1206.3679 |