Sizes of flat maximal antichains of subsets
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910504814903296 |
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| author | Griggs, Jerrold R. Kalinowski, Thomas Leck, Uwe Roberts, Ian T. Schmitz, Michael |
| author_facet | Griggs, Jerrold R. Kalinowski, Thomas Leck, Uwe Roberts, Ian T. Schmitz, Michael |
| contents | This is the second of two papers investigating for which positive integers $m$ there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$ (the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion). In the first part, the sizes of maximal antichains have been characterized. Here we provide an alternative construction with the benefit of showing that almost all sizes of maximal antichains can be obtained using antichains containing only $l$-sets and $(l+1)$-sets for some $l$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07062 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sizes of flat maximal antichains of subsets Griggs, Jerrold R. Kalinowski, Thomas Leck, Uwe Roberts, Ian T. Schmitz, Michael Combinatorics Discrete Mathematics 06A07 This is the second of two papers investigating for which positive integers $m$ there exists a maximal antichain of size $m$ in the Boolean lattice $B_n$ (the power set of $[n]:=\{1,2,\dots,n\}$, ordered by inclusion). In the first part, the sizes of maximal antichains have been characterized. Here we provide an alternative construction with the benefit of showing that almost all sizes of maximal antichains can be obtained using antichains containing only $l$-sets and $(l+1)$-sets for some $l$. |
| title | Sizes of flat maximal antichains of subsets |
| topic | Combinatorics Discrete Mathematics 06A07 |
| url | https://arxiv.org/abs/2302.07062 |