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Automorphism groups of posets with forbidden subposets

✍ Scribed by Gerhard Behrendt

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 786 KB
Volume: 105
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90127-2

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✦ Synopsis

Behrendt, G., Automorphism groups of posets with forbidden subposets, Discrete Mathematics 105 (1992) 1-11.

We show that there exists a finite set S of finite posets such that the following holds. Whenever, (Y, s) is not isomorphic to a member of S and it is not trivially ordered then for every finite group G there exists a finite poset (X, C) which has no induced subposet isomorphic to (Y, C) such that G is isomorphic to the automorphism group of (X, s). For some members (Y, s) of S we give necessary and sufficient conditions for a group G to be isomorphic to the automorphism group of a finite poset (X, s) which has no induced subposet (Y, c). This includes the classification of the automorphism groups of finite interval orders and seriesparallel posets.

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