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Is there a name for a subset $\{x_i\}$ of a poset $(P,\leq)$ satisfying $x_1 \leq x_2 \geq x_3 \leq \cdots \geq x_{n-1} \leq x_n$? (The subset could be infinite and the inequalities could be strict.)

I'm quite sure there's a name for this (although maybe not too popular) but I can't remember. Thanks.

Abel
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    I've seen such things referred to as crowns. – Mariano Suárez-Álvarez May 31 '14 at 03:03
  • @Mariano: I think there are more order relations in a crown (see http://designtheory.org/library/encyc/topics/posets.pdf). – Qiaochu Yuan May 31 '14 at 03:17
  • @QiaochuYuan, the term has not a fixed sense. Those crowns are definitely not what the people I heard use the term meant. I've also seen people complain that a crown should be round, meaning that the name only fits if also x_n is larger than x_1 (fence does seem more appropriate in that respect...) – Mariano Suárez-Álvarez May 31 '14 at 03:42

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Thanks to Mariano Suárez-Alvarez's comment, I found the term I was looking for: fence.

Abel
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