TY - JOUR
T1 - New bounds on the maximum size of Sperner partition systems
AU - Chang, Yanxun
AU - Colbourn, Charles J.
AU - Gowty, Adam
AU - Horsley, Daniel
AU - Zhou, Junling
N1 - Funding Information:
Much of this research was undertaken during visits by C.J. Colbourn and D. Horsley to Beijing Jiaotong University. They express their sincere thanks to the 111 Project of China ( B16002 ) for financial support and to the Department of Mathematics at Beijing Jiaotong University for their kind hospitality. The authors’ research received support from the following sources. Y. Chang: NSFC grant 11971053 ; C.J. Colbourn: NSF grants 1421058 and 1813729 ; A. Gowty: Australian Government Research Training Program Scholarship ; D. Horsley: ARC grants DP150100506 and FT160100048 ; J. Zhou: NSFC grant 11571034 .
Funding Information:
Much of this research was undertaken during visits by C.J. Colbourn and D. Horsley to Beijing Jiaotong University. They express their sincere thanks to the 111 Project of China (B16002) for financial support and to the Department of Mathematics at Beijing Jiaotong University for their kind hospitality. The authors? research received support from the following sources. Y. Chang: NSFC grant 11971053; C.J. Colbourn: NSF grants 1421058 and 1813729; A. Gowty: Australian Government Research Training Program Scholarship; D. Horsley: ARC grants DP150100506 and FT160100048; J. Zhou: NSFC grant 11571034.
PY - 2020/12
Y1 - 2020/12
N2 - 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 SP(n,k). In this paper we introduce a new construction for Sperner partition systems and use it to asymptotically determine SP(n,k) in many cases as [Formula presented] becomes large. We also give a slightly improved upper bound for SP(n,k) and exhibit an infinite family of parameter sets (n,k) for which this bound is tight.
AB - 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 SP(n,k). In this paper we introduce a new construction for Sperner partition systems and use it to asymptotically determine SP(n,k) in many cases as [Formula presented] becomes large. We also give a slightly improved upper bound for SP(n,k) and exhibit an infinite family of parameter sets (n,k) for which this bound is tight.
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U2 - 10.1016/j.ejc.2020.103165
DO - 10.1016/j.ejc.2020.103165
M3 - Article
AN - SCOPUS:85087746459
VL - 90
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
M1 - 103165
ER -