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On Families of Subsets With a Forbidden Subposet

Published online by Cambridge University Press:  01 September 2009

JERROLD R. GRIGGS  and
LINYUAN LU
JERROLD R. GRIGGS
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA (e-mail: [email protected], [email protected])
LINYUAN LU
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA (e-mail: [email protected], [email protected])
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Abstract

Let ⊂ 2[n] be a family of subsets of {1, 2,. . ., n}. For any poset H, we say is H-free if does not contain any subposet isomorphic to H. Katona and others have investigated the behaviour of La(n, H), which denotes the maximum size of H-free families ⊂ 2[n]. Here we use a new approach, which is to apply methods from extremal graph theory and probability theory to identify new classes of posets H, for which La(n, H) can be determined asymptotically as n → ∞ for various posets H, including two-end-forks, up-down trees, and cycles C4k on two levels.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 5: New Directions in Algorithms, Combinatorics and Optimization , September 2009 , pp. 731 - 748
Copyright
Copyright © Cambridge University Press 2009

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