| Title: | Chromatic numbers, Buchstaber numbers and chordality of Bier spheres |
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| Authors: | ID Limonchenko, Ivan (Author)
ID Vavpetič, Aleš (Author) |
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| Files: |  PDF - Presentation file, download (1,06 MB)
MD5: B4A761DBA0231F855AE484A4A3037E31
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0012365X2600213X
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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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 $d \ge 0$. Then we prove a general formula for complex and mod $p$ Buchstaber numbers of a Bier sphere ${\rm Bier}(K)$, 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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| Keywords: | Bier sphere, Buchstaber number, chordal graph, chromatic number, stacked polytope |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.09.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 349, iss. 9, article no. 115189 |
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| PID: | 20.500.12556/DiRROS-29281  |
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| UDC: | 519.17:514 |
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| ISSN on article: | 0012-365X |
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| DOI: | 10.1016/j.disc.2026.115189 |
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| COBISS.SI-ID: | 277148675 |
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| Publication date in DiRROS: | 06.05.2026 |
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| Views: | 121 |
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| Downloads: | 74 |
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