, Volume 24, Issue 2, pp 133–138 | Cite as

Infinitely Many Trees Have Non-Sperner Subtree Poset



Let C(T) denote the poset of subtrees of a tree T with respect to the inclusion ordering. Jacobson, Kézdy and Seif gave a single example of a tree T for which C(T) is not Sperner, answering a question posed by Penrice. The authors then ask whether there exist an infinite family of trees T such that C(T) is not Sperner. This paper provides such a family.


Poset Lattice Sperner property Subtree 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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