Timeline for The name for a partial order
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 23, 2014 at 19:25 | comment | added | Russ Woodroofe | See also this question mathoverflow.net/questions/76723/… | |
| Aug 31, 2011 at 19:30 | comment | added | Richard Stanley | @Victor, I don't know any interesting theorems about order ideals of $M(n)$. The fact that every antichain is finite also follows from a general result of Higman; see Exercise 3.13(a) of math.mit.edu/~rstan/ec/ec1.pdf. There are some nice results concerning multichains in $M(n)$. | |
| Aug 8, 2011 at 17:42 | comment | added | Gerhard Paseman | A little more: the paper of Polak's had to be in the late 70's or early 80's. An additional fact which I needed and later found he proved was that the order had only finite antichains, and no infinite antichains. Perhaps you are willing to post another question on what statements about order ideals you hope are theorems about M(infinity)? Gerhard "Inquiring Minds Like To Know" Paseman, 2011.08.08 | |
| Aug 7, 2011 at 16:17 | comment | added | Victor Miller | @Richard, Thanks so much! Since there's an obvious inclusion $M(n) \rightarrow M(n+1)$ so that we have the direct limit $M(\infty)$. I'm interested in theorems about order ideals in $M(n)$. Can you supply any references? | |
| Aug 7, 2011 at 0:12 | comment | added | Richard Stanley | In combinatorics this poset, restricted to subsets of {1,2...,n}, is denoted $M(n)$. For an application, see Sections 4.1.2-4.1.3 of math.mit.edu/~rstan/pubs/pubfiles/84.pdf. | |
| Aug 6, 2011 at 20:57 | comment | added | Kaveh | might help we think of the finite subsets as finite increasing sequences, and considering point-wise ordering. | |
| Aug 6, 2011 at 19:53 | comment | added | Victor Miller | @Gerald, Thanks. I'll have to wait until Monday -- my copy is at work. | |
| Aug 6, 2011 at 19:52 | history | edited | Victor Miller | CC BY-SA 3.0 |
Added links to Kundgen's and my paper
|
| Aug 6, 2011 at 19:51 | comment | added | Gerald Edgar | Perhaps a relative of the order in the last chapter of Hardy, Littlewood, Polya, Inequalities | |
| Aug 6, 2011 at 19:46 | comment | added | Gerhard Paseman | I took the liberty of adding the universal-algebra tag, as both Libor Polak and I were doing work in that field. It would not surprise me if the order occurred in some earlier papers in model theory as well, but that's a guess on my part. Gerhard "Ask Me About System Design" Paseman, 2011.08.06 | |
| Aug 6, 2011 at 19:45 | comment | added | Victor Miller | @Gerhard, Thanks. And I didn't realize that it had anything to do with Universal Algebra! | |
| Aug 6, 2011 at 19:43 | history | edited | Gerhard Paseman |
edited tags
|
|
| Aug 6, 2011 at 19:37 | comment | added | Gerhard Paseman | This looks like the partial order I used for my dissertation for ordering signatures of finite functional languages. I did not come up with a name for it, but I used the fact that it was well founded (and maybe some other property) to show that a certain class of sets was a class of recursive sets. Although I came up with my own proof of these properties, Libor Polak (who essentially simultaneously discovered one of the results of my dissertation) had proven these properties years before. He might know of a name. Gerhard "Ask Me About System Design" Paseman, 2011.08.05 | |
| Aug 6, 2011 at 19:29 | history | edited | Victor Miller |
Fixed tags
|
|
| Aug 6, 2011 at 19:24 | history | asked | Victor Miller | CC BY-SA 3.0 |