Timeline for Proving that a poset is a lattice
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2022 at 11:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Mar 17, 2013 at 6:36 | vote | accept | Martin Rubey | ||
| Oct 11, 2010 at 20:21 | comment | added | Martin Rubey | I just discovered yet another local criterion, by Günther Ziegler, in "a new local criterion for the lattice property" (Algebra Universalis, Volume 31, Number 4, 608-610, 1994): if x1, x2 cover x and y1, y2 are covered by y, and x1, x2 <= y1, y2, then there is a z such that x1, x2 < z < y1, y2. (unfortunately, I still didn't manage to prove the lattice property in the problem at hand) | |
| Sep 29, 2010 at 6:50 | comment | added | Martin Rubey | This is awesome! Namely, if x and y cover a common element, it turns out to be relatively easy to describe the (conjectural) join. Thus, it "only" remains to prove that all other common upper bounds of x and y are larger. I'm curious whether I'll be able to do it... | |
| Sep 28, 2010 at 18:42 | history | answered | David E Speyer | CC BY-SA 2.5 |