Analyzing Subuniverse Counts in Finite Semilattices: Unveiling the Rankings and Descriptions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929463452762112 |
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| author | Ahmed, Delbrin Salih, Muwafaq Haje, Dilbak |
| author_facet | Ahmed, Delbrin Salih, Muwafaq Haje, Dilbak |
| contents | Let $(L,\vee)$ be a finite n-element semilattice where $n\geq 5$. We prove that the fourth largest number of subuniverses of an $n$-element semilattice is $25\cdot 2^{n-5}$, the fifth largest number is $ 24.5\cdot 2^{n-5}$, and the sixth one is $ 24\cdot 2^{n-5}$. Also, we describe the $n$-element semilattices with exactly $25\cdot 2^{n-5}$, $ 24.5\cdot 2^{n-5}$ or $ 24\cdot 2^{n-5}$ subuniverses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analyzing Subuniverse Counts in Finite Semilattices: Unveiling the Rankings and Descriptions Ahmed, Delbrin Salih, Muwafaq Haje, Dilbak Combinatorics Let $(L,\vee)$ be a finite n-element semilattice where $n\geq 5$. We prove that the fourth largest number of subuniverses of an $n$-element semilattice is $25\cdot 2^{n-5}$, the fifth largest number is $ 24.5\cdot 2^{n-5}$, and the sixth one is $ 24\cdot 2^{n-5}$. Also, we describe the $n$-element semilattices with exactly $25\cdot 2^{n-5}$, $ 24.5\cdot 2^{n-5}$ or $ 24\cdot 2^{n-5}$ subuniverses. |
| title | Analyzing Subuniverse Counts in Finite Semilattices: Unveiling the Rankings and Descriptions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.09595 |