Timeline for Is every finite lattice isomorphic to a union-closed family of sets containing $\emptyset$?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15 at 14:27 | answer | added | Gavin Wraith | timeline score: 1 | |
| Apr 14 at 17:53 | comment | added | Sam Hopkins | @ClayThomas: sorry, I decided these comments actually made sense as an answer to the related question mathoverflow.net/questions/450680. By the way now you can see that all Stanley did for the answer for this question is to take complements for the answer to that one (changing an intersection-closed family to a union-closed family). | |
| Apr 14 at 17:30 | comment | added | Clay Thomas | For some reason SamHopkins's comments are gone. He recommended the references ams.org/journals/tran/1975-203-00/S0002-9947-1975-0360386-3 and arxiv.org/pdf/1712.10123.pdf which indeed look relevant for the general context (even if not giving the specific answer) | |
| Apr 14 at 17:27 | vote | accept | Clay Thomas | ||
| Apr 14 at 15:34 | answer | added | Richard Stanley | timeline score: 5 | |
| Apr 14 at 15:12 | comment | added | Clay Thomas | Thanks @SamHopkins and @GeraldEdgar! Not sure about Birkhoff's book, but it looks like [Birkhoff & Frink 1947] "Representations of lattices by sets" contains the result with a slightly more involved construction. I found that paper via the references in the [Thomas & Williams] arxiv link - looks like a useful way of thinking of things which I'll keep picking through - thanks! | |
| Apr 14 at 12:13 | comment | added | Gerald Edgar | Stanley's observation is also presumably in Birkhoff's Lattice Theory (1940). | |
| Apr 14 at 6:26 | comment | added | Clay Thomas | @RichardStanley wow! Very simple - thank you. If you'd like to copy your comment into an answer (just to 'check the box' etc) that would be excellent | |
| Apr 13 at 23:40 | comment | added | Richard Stanley | Given $x\in L$, let $S_x=\{y\in L\,:\,y\not\geq x\}$. | |
| Apr 13 at 22:11 | comment | added | Clay Thomas | @mathworker21 care to elaborate? | |
| Apr 13 at 22:00 | comment | added | mathworker21 | yes ${}{}{}{}{}$ | |
| Apr 13 at 21:33 | history | asked | Clay Thomas | CC BY-SA 4.0 |