Talk:Fence (mathematics)
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Issues with equivalent conditions
editI believe much of what is written in the section `Equivalent conditions' is incorrect.
Echoing this above, the statements in this section are in fact wrong. — Preceding unsigned comment added by 81.141.89.112 (talk) 14:44, 16 November 2021 (UTC)
- I haven't looked at all the conditions closely, but it is obviously false that a poset where every element is either minimal or maximal has to be a disjoint union of zigzag posets. Consider the poset with four elements with
- a<d, b<d, c<d and a,b,c incomparable.
- It's probably true that any such poset is obtained by a disjoint union of zigzag posets by adding relations of the form m < M, where m is a minimal element of one zigzag poset and M a maximal element of an other. 146.111.156.63 (talk) 21:04, 13 May 2024 (UTC)
- I removed the obviously-false condition (I agree) but the rest need careful examination and sourcing. —David Eppstein (talk) 21:34, 13 May 2024 (UTC)
Example request
editAn example of a fence would be a lovely addition to the article. Charibdis (talk) 00:09, 9 January 2011 (UTC)
Commutative rings
editCan you give examples of commutative rings of Krull dimension 1 for which the poset of prime ideals, ordered by inclusion, is a fence? GeoffreyT2000 (talk) 02:32, 5 May 2015 (UTC)
- You're the one who added Krull dimension to the article. Shouldn't you be the one to find sources and examples for that connection? —David Eppstein (talk) 03:10, 5 May 2015 (UTC)
- Well, I have several examples, such as discrete valuation rings. GeoffreyT2000 (talk) 04:29, 5 May 2015 (UTC)
- With sources? Please don't add material unless you can source it properly. —David Eppstein (talk) 04:50, 5 May 2015 (UTC)
- Well, I have several examples, such as discrete valuation rings. GeoffreyT2000 (talk) 04:29, 5 May 2015 (UTC)
Wrong counting sequence
editShouldn't the correct counting sequence be 1, 1, 1, 2, 5, 16, 61, 272, 1385, ... with reference to the OEIS sequence number A000111? This is half the number of alternating permutations (A001250). Also, the bijection between half of the alternating permutations and linear extensions of a fence is not immediately clear to me, even though there should be an easy argument. Torsten Mütze (talk) 16:26, 11 June 2019 (UTC)