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arXiv · 2602.11352

On the combinatorics of Murai spheres and its applications

Ivan Limonchenko·Aleš Vavpetič
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Abstract

We classify the combinatorial types of Murai spheres in dimensions $1$ and $2$, thereby showing that the corresponding convex simple polytopes have Delzant realizations. Then we describe all chordal Murai spheres $\mathrm{Bier}_c(M)$ with $c\in\mathbb N^m$ and $m\leq 2$. Finally, we find all possible values for the Buchstaber and chromatic numbers of arbitrary Murai spheres.

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Ivan Limonchenko, Aleš Vavpetič. 2026-02-11. On the combinatorics of Murai spheres and its applications. https://arxiv.org/abs/2602.11352

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