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arXiv · 2412.20861

Chromatic numbers, Buchstaber numbers and chordality of Bier spheres

Ivan Limonchenko·Aleš Vavpetič
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Abstract

We describe all the Bier spheres of dimension $d$ with chromatic number equal to $d+1$ and prove that all other $d$-dimensional Bier spheres have chromatic number equal to $d+2$, for any integer $d\geq 0$. Then we prove a general formula for complex and mod $p$ Buchstaber numbers of a Bier sphere $\mathrm{Bier}(K)$, for each prime $p\in\mathbb{N}$ in terms of the $f$-vector of the underlying simplicial complex $K$. Finally, we classify all chordal Bier spheres and obtain their canonical realizations as boundaries of stacked polytopes.

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Ivan Limonchenko, Aleš Vavpetič. 2026-02-16. Chromatic numbers, Buchstaber numbers and chordality of Bier spheres. https://arxiv.org/abs/2412.20861

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