Associating hypergraphs defined on loops
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914928852467712 |
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| author | Malviy, Siddharth Kakkar, Vipul |
| author_facet | Malviy, Siddharth Kakkar, Vipul |
| contents | In this paper, we define a new hypergraph $\mathcal{H(V,E)}$ on a loop $L$, where $\mathcal{V}$ is the set of points of the loop $L$ and $\mathcal{E}$ is the set of hyperedges $e=\{x,y,z\}$ such that $x,y$ and $z$ associate in the order they are written. We call this hypergraph as the associating hypergraph on a loop $L$. We study certain properites of associating hypergraphs on the Moufang loop $M(D_n,2)$, where $D_n$ denotes the dihedral group of order $2n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Associating hypergraphs defined on loops Malviy, Siddharth Kakkar, Vipul Combinatorics Group Theory In this paper, we define a new hypergraph $\mathcal{H(V,E)}$ on a loop $L$, where $\mathcal{V}$ is the set of points of the loop $L$ and $\mathcal{E}$ is the set of hyperedges $e=\{x,y,z\}$ such that $x,y$ and $z$ associate in the order they are written. We call this hypergraph as the associating hypergraph on a loop $L$. We study certain properites of associating hypergraphs on the Moufang loop $M(D_n,2)$, where $D_n$ denotes the dihedral group of order $2n$. |
| title | Associating hypergraphs defined on loops |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2408.16459 |