(1+1+2)-generated lattices of quasiorders
| Autor: | Ahmed, Delbrin, Cz��dli, G��bor |
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| Rok vydání: | 2021 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2104.14653 |
| Popis: | A lattice is $(1+1+2)$-generated if it has a four-element generating set such that exactly two of the four generators are comparable. We prove that the lattice Quo$(n)$ of all quasiorders (also known as preorders) of an $n$-element set is $(1+1+2)$-generated for $n=3$ (trivially), $n=6$ (when Quo(6) consists of $209\,527$ elements), n=11, and for every natural number $n\geq 13$. In 2017, the second author and J. Kulin proved that Quo$(n)$ is $(1+1+2)$-generated if either $n$ is odd and at least $13$ or $n$ is even and at least $56$. Compared to the 2017 result, this paper presents twenty-four new numbers $n$ such that Quo$(n)$ is $(1+1+2)$-generated. Except for Quo(6), an extension of Z��dori's method is used. 14 pages, 4 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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