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New bounds on the maximum size of Sperner partition systems
- Source :
- European J. Combin. 90 (2020), 103165, 18 pp
- Publication Year :
- 2018
-
Abstract
- An $(n,k)$-Sperner partition system is a collection of partitions of some $n$-set, each into $k$ nonempty classes, such that no class of any partition is a subset of a class of any other. The maximum number of partitions in an $(n,k)$-Sperner partition system is denoted $\mathrm{SP}(n,k)$. In this paper we introduce a new construction for Sperner partition systems and use it to asymptotically determine $\mathrm{SP}(n,k)$ in many cases as $\frac{n}{k}$ becomes large. We also give a slightly improved upper bound for $\mathrm{SP}(n,k)$ and exhibit an infinite family of parameter sets $(n,k)$ for which this bound is tight.<br />Comment: 20 pages, 2 figures
- Subjects :
- Mathematics - Combinatorics
05D05 (Primary)
Subjects
Details
- Database :
- arXiv
- Journal :
- European J. Combin. 90 (2020), 103165, 18 pp
- Publication Type :
- Report
- Accession number :
- edsarx.1811.03731
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.ejc.2020.103165