Infinitely Many Trees Have Non-Sperner Subtree Poset

Andrew Vince; Hua Wang

doi:10.1007/s11083-007-9064-2

Infinitely Many Trees Have Non-Sperner Subtree Poset

Andrew Vince, Hua Wang

Mathematical Sciences

University of Florida

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	American English
Journal	Order
Volume	24
DOIs	https://doi.org/10.1007/s11083-007-9064-2
State	Published - May 2007

Disciplines

Mathematics

Keywords

Non-sperner subtree poset
Trees

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10.1007/s11083-007-9064-2License: Unspecified

Cite this

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title = "Infinitely Many Trees Have Non-Sperner Subtree Poset",

abstract = " Let C ( T ) denote the poset of subtrees of a tree T with respect to the inclusion ordering. Jacobson, K{\'e}zdy 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.",

keywords = "Non-sperner subtree poset, Trees",

author = "Andrew Vince and Hua Wang",

note = "Let C( T) denote the poset of subtrees of a tree T with respect to the inclusion ordering. Jacobson, K{\'e}zdy and Seif gave a single example of a tree T for which C( T) is not Sperner, answering a...",

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AU - Vince, Andrew

AU - Wang, Hua

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PY - 2007/5

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N2 - 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.

AB - 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.

KW - Non-sperner subtree poset

KW - Trees

UR - https://doi.org/10.1007/s11083-007-9064-2

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DO - 10.1007/s11083-007-9064-2

M3 - Article

SN - 0167-8094

VL - 24

JO - Order

JF - Order

ER -

Infinitely Many Trees Have Non-Sperner Subtree Poset

Abstract

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Keywords

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