Frankl's Conjecture for a subclass of semimodular lattices
| Autor: | Vinayak Joshi, Baloo Waphare |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 11, Iss Special Issue Dedicated to Prof. George A. Gratzer, Pp 197-206 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2345-5853 2345-5861 |
| DOI: | 10.29252/cgasa.11.1.197 |
| Popis: | In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)\setminus A(L)| \leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices having breadth at most two. We provide a very short proof of the Conjecture for the class of lattices having breadth at most two. This generalizes the results of Joshi, Waphare and Kavishwar as well as Czédli and Schmidt. |
| Databáze: | Directory of Open Access Journals |
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