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 - Publisher Copyright:
© 2020
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
SN - 0195-6698
VL - 90
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103165
ER -