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dedicated to professor jack k. hale on the occasion of his 70th birthday We study the map 9: C 2 Ä C 2 defined by 9(w, z)=(z, z+w 2) and the associated collection of sequences [z j ] satisfying the recurrence z j+2 =z j+1 +z 2 j. Iteration of 9 is equivalent to the study of such sequences. We analyze growth rates of the sequences, positive sequences,… (More)

- Brenda J Latka, Nathaniel Dean, Paul Seymour, Peter Winkler Discussions, Stephen Greenfield, Tom Yuster
- 2002

Tournament embedding is an order relation on the class of finite tournaments. An antichain is a set of finite tournaments that are pairwise incomparable in this ordering. We say an antichain A can be extended to an antichain B if A ⊆ B. Those finite antichains that can not be extended to antichains of arbitrarily large finite cardinality are exactly those… (More)

The maximum antichain cardinality (MACC) of a tournament is the maximum number of in-comparable subtournaments of T. We establish some properties of MACC. We describe all tournaments whose MACC is 1 or 2, show that MACC can grow exponentially with the size of the vertex set of a tournament, and present some questions for further investigation. A tournament… (More)

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