A characterization of permutability of 2-uniform tolerances on posets
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910332263333888 |
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| author | Chajda, Ivan Länger, Helmut |
| author_facet | Chajda, Ivan Länger, Helmut |
| contents | Tolerance relations were investigated by several authors in various algebraic structures, see e.g. the monograph by I. Chajda. Recently G. Czédli studied so-called 2-uniform tolerances on lattices, i.e. tolerances that are compatible with the lattice operations and whose blocks are of cardinality 2. He showed that two such tolerances on a lattice containing no infinite chain permute if and only if they are amicable (a concept introduced in his paper). We extend this study to tolerances on posets. Since in posets we have no lattice operations, we must modify the notion of amicability. We modified it in such a way that in case of lattices it coincides with the original definition. With this new definition we can prove that two tolerances on a poset containing no infinite chain permute if and only if they are amicable in the new sense. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_09496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of permutability of 2-uniform tolerances on posets Chajda, Ivan Länger, Helmut Combinatorics 08A02, 08A05, 06A06, 06A11 Tolerance relations were investigated by several authors in various algebraic structures, see e.g. the monograph by I. Chajda. Recently G. Czédli studied so-called 2-uniform tolerances on lattices, i.e. tolerances that are compatible with the lattice operations and whose blocks are of cardinality 2. He showed that two such tolerances on a lattice containing no infinite chain permute if and only if they are amicable (a concept introduced in his paper). We extend this study to tolerances on posets. Since in posets we have no lattice operations, we must modify the notion of amicability. We modified it in such a way that in case of lattices it coincides with the original definition. With this new definition we can prove that two tolerances on a poset containing no infinite chain permute if and only if they are amicable in the new sense. |
| title | A characterization of permutability of 2-uniform tolerances on posets |
| topic | Combinatorics 08A02, 08A05, 06A06, 06A11 |
| url | https://arxiv.org/abs/2402.09496 |