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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11907 |
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Table of Contents:
- This paper investigates five kinds of systems of $d$-partitions of $[n]$, including symmetric Bollobás systems, strong Bollobás systems, Bollobás systems, skew Bollobás systems, and weak Bollobás systems. Many known results on variations of Bollobás systems are unified. Especially we give a negative answer to a conjecture on Bollobás systems of $d$-partitions of $[n]$ that was presented by Hegedüs and Frankl [European J. Comb., 120 (2024), 103983]. Even though this conjecture does not hold for general Bollobás systems, we show that it holds for strong Bollobás systems of $d$-partitions of $[n]$.