Timeline for answer to Combinatorics problem related to Motzkin numbers with prize money I by FindStat
Current License: CC BY-SA 4.0
Post Revisions
25 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2019 at 7:26 | comment | added | Christian Stump | @Vincent: done, thanks for pinging! | |
| Nov 26, 2019 at 7:26 | history | edited | Christian Stump | CC BY-SA 4.0 |
updated broken link
|
| Nov 24, 2019 at 23:02 | comment | added | Vincent | The link to the temporary storing place of the paper doesn't work anymore. Could you add the link to the Arxiv-version? | |
| Aug 18, 2017 at 14:07 | history | bounty awarded | Mare | ||
| Aug 17, 2017 at 2:25 | vote | accept | Mare | ||
| Aug 16, 2017 at 22:03 | history | edited | Martin Rubey | CC BY-SA 3.0 |
provide paper
|
| Aug 10, 2017 at 22:04 | history | edited | Martin Rubey | CC BY-SA 3.0 |
include outline of proof
|
| S Aug 10, 2017 at 16:02 | history | suggested | Christian Stump | CC BY-SA 3.0 |
added that we know how to do it.
|
| Aug 10, 2017 at 15:54 | review | Suggested edits | |||
| S Aug 10, 2017 at 16:02 | |||||
| Aug 10, 2017 at 7:49 | comment | added | Martin Rubey | @SylvainJULIEN: sorry, I do not understand your question. As far as I can see, the remaining difficulty is to translate the second condition of a $2$-Gorenstein failure $(a,b)$ into the Dyck path picture. The permutation matrix is easy to see in this picture: drawing the Dyck path with north and east steps, staying above the main diagonal, put a cross into each valley and fill the remaining slots with an increasing sequence. | |
| Aug 9, 2017 at 23:24 | comment | added | Mare | @MartinRubey the condition $c_{a+b} \geq c_{a+b-1}$ alone also has an interesting interpretation. If I made no mistake it counts the algebras having the double centralizer protperty with respect to a minimal faithful projective-injective module. My conjecture is that the corresponding sequence is oeis.org/A005043 . | |
| Aug 9, 2017 at 22:56 | comment | added | Martin Rubey | It appears that Sergi Elizalde's cycle diagram makes at least the relation between $c_{a+b}\geq c_{a+b-1}$ and double deficiencies clear. I haven't translated the other condition yet, though. | |
| S Aug 9, 2017 at 20:57 | history | edited | FindStat | CC BY-SA 3.0 |
added code
|
| S Aug 9, 2017 at 20:57 | history | suggested | Christian Stump | CC BY-SA 3.0 |
added code
|
| Aug 9, 2017 at 20:52 | review | Suggested edits | |||
| S Aug 9, 2017 at 20:57 | |||||
| Aug 9, 2017 at 20:45 | comment | added | Sylvain JULIEN | I don't quite get it. Wouldn't it follow from the fact that a pair $ (a,b) $ is either 2-Gorenstein or a 2-Gorenstein failure and if $ i\neq\sigma(i) $ then $\sigma( i )$ is either a double deficiency or a double excedance ? I must be missing something. | |
| Aug 9, 2017 at 20:34 | comment | added | Mare | Yes, more information is always better. | |
| Aug 9, 2017 at 20:33 | comment | added | Christian Stump | I think it would be useful to add the code here as it is rather straightforward to see how this works. Should I add it? | |
| Aug 9, 2017 at 20:32 | comment | added | Martin Rubey | @Mare: I checked all Dyck paths with semilength at most 11. | |
| Aug 9, 2017 at 20:27 | comment | added | Martin Rubey | @SylvainJULIEN: yes, you only need to reverse inequalities. | |
| Aug 9, 2017 at 20:21 | comment | added | Sylvain JULIEN | I can read in your second link the definition of a double deficiency but not of a double excedance : is it the same with reversed inequalities, i. e a "negative" double deficiency ? | |
| Aug 9, 2017 at 20:20 | comment | added | Mare | This looks spectacular. How good tested is your conjecture? | |
| Aug 9, 2017 at 20:10 | history | edited | Martin Rubey | CC BY-SA 3.0 |
correct conjecture
|
| Aug 9, 2017 at 19:55 | review | First posts | |||
| Aug 9, 2017 at 20:08 | |||||
| Aug 9, 2017 at 19:54 | history | answered | FindStat | CC BY-SA 3.0 |