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arXiv · 2407.13959

Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ ]{Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$

Matthew J. Fyfe·Steven R. Lippold·Mihai D. Staic·Alin Stancu
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Abstract

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 $det^{S^2}$.

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BibTeXRIS

Matthew J. Fyfe, Steven R. Lippold, Mihai D. Staic, Alin Stancu. 2024-07-19. Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$ ]{Twin-star hypothesis and cycle-free $d$-partitions of $K_{2d}$. https://arxiv.org/abs/2407.13959

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