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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2407.18167 |
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| _version_ | 1866929437199564800 |
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| author | Kunos, Ádám Larose, Benoit Pullas, David Emmanuel Pazmiño |
| author_facet | Kunos, Ádám Larose, Benoit Pullas, David Emmanuel Pazmiño |
| contents | Call a finite relational structure $k$-Slupecki if its only surjective $k$-ary polymorphisms are essentially unary, and Slupecki if it is $k$-Slupecki for all $k \geq 2$. We present conditions, some necessary and some sufficient, for a reflexive digraph to be Slupecki. We prove that all digraphs that triangulate a 1-sphere are Slupecki, as are all the ordinal sums $m \oplus n$ ($m,n \geq 2$). We prove that the posets $P = m \oplus n \oplus k$ are not 3-Slupecki for $m,n,k \geq 2$, and prove there is a bound $B(m,k)$ such that $P$ is 2-Slupecki if and only if $n > B(m,k)+1$; in particular there exist posets that are 2-Slupecki but not 3-Slupecki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Słupecki Digraphs Kunos, Ádám Larose, Benoit Pullas, David Emmanuel Pazmiño Combinatorics 08 Call a finite relational structure $k$-Slupecki if its only surjective $k$-ary polymorphisms are essentially unary, and Slupecki if it is $k$-Slupecki for all $k \geq 2$. We present conditions, some necessary and some sufficient, for a reflexive digraph to be Slupecki. We prove that all digraphs that triangulate a 1-sphere are Slupecki, as are all the ordinal sums $m \oplus n$ ($m,n \geq 2$). We prove that the posets $P = m \oplus n \oplus k$ are not 3-Slupecki for $m,n,k \geq 2$, and prove there is a bound $B(m,k)$ such that $P$ is 2-Slupecki if and only if $n > B(m,k)+1$; in particular there exist posets that are 2-Slupecki but not 3-Slupecki. |
| title | Słupecki Digraphs |
| topic | Combinatorics 08 |
| url | https://arxiv.org/abs/2407.18167 |