Centre for Discrete and Applicable Mathematics

CDAM Research Report, LSE-CDAM-97-16

December 1997

Forbidden Induced Partial Orders

Graham Brightwell, David A. Grable, and Hans Jürgen Prömel

Abstract

For each finite partial order P, we consider the size of the set Forb_indⁿ(P) of partial orders on n labelled points containing no induced copy of P. We show that |Forb_indⁿ(P)| = 2^o(n²) unless P has height at least 3, in which case |Forb_indⁿ(P)| = 2^n²/4+o(n²). We show that |Forb_indⁿ(P)| <= n! c for some constant c if and only if P is either an antichain or one of ten small partial orders. Between these extremes, we consider the question of which P have |Forb_indⁿ(P)| = n^O(n).

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		CDAM Research Reports Series Centre for Discrete and Applicable Mathematics London School of Economics Houghton Street London WC2A 2AE, U.K.
		Phone: +44(0)-171-955 7732. Fax: +44(0)-171-955 6877. Email: info@maths.lse.ac.uk