Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ ]{Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909262120222720 |
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| author | Fyfe, Matthew J. Lippold, Steven R. Staic, Mihai D. Stancu, Alin |
| author_facet | Fyfe, Matthew J. Lippold, Steven R. Staic, Mihai D. Stancu, Alin |
| contents | In this paper we study an equivalence relation defined on the set of cycle-free $d$-partitions of the complete graph $K_{2d}$. We discuss a conjecture which states that this equivalence relation has only one equivalence class, and show that the conjecture is equivalent with the so called twin-star hypothesis. We check the conjecture in the case $d=4$ and disuses how this relates to the determinant-like map $det^{S^2}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ ]{Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ Fyfe, Matthew J. Lippold, Steven R. Staic, Mihai D. Stancu, Alin Combinatorics Primary 05C70, Secondary 05E18 In this paper we study an equivalence relation defined on the set of cycle-free $d$-partitions of the complete graph $K_{2d}$. We discuss a conjecture which states that this equivalence relation has only one equivalence class, and show that the conjecture is equivalent with the so called twin-star hypothesis. We check the conjecture in the case $d=4$ and disuses how this relates to the determinant-like map $det^{S^2}$. |
| title | Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ ]{Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ |
| topic | Combinatorics Primary 05C70, Secondary 05E18 |
| url | https://arxiv.org/abs/2407.13959 |