Chromatic numbers, Buchstaber numbers and chordality of Bier spheres
| Autor: | Limonchenko, Ivan, Vavpetič, Aleš |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 18 pages, 7 figures |
| Databáze: | arXiv |
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