Timeline for Sequence that sums up to the number of permutations avoiding the pattern $1-23-4$
Current License: CC BY-SA 4.0
9 events
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| May 17, 2023 at 17:05 | comment | added | Martin Rubey |
I just see that A258173 does not really define a subset of Dyck paths. So it is less clear how to turn b into a distribution on Dyck paths.
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| May 17, 2023 at 17:04 | comment | added | Notamathematician | Unfortunately, I don't really understand how it works. Сould you help me here too? You could post the answer on the page of my other question: mathoverflow.net/questions/446148/…. | |
| May 17, 2023 at 16:59 | comment | added | Martin Rubey |
Dyck paths are actually the collection with the greatest number of statistics in the database. Do you want to try your luck? You only have to adapt the definition of avd and dst above.
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| May 17, 2023 at 16:57 | comment | added | Notamathematician | Thank you again! If we change $(k+1)$ to $(k+2)$, we get A258173 as a result. The description provides a combinatorial interpretation through rooted trees. Does FindStat only work with permutations and binary words, or can we also get a result for this case? | |
| May 17, 2023 at 16:42 | comment | added | Martin Rubey | Yes, the code above works, there is no more input required. I do set the maximal number of transformations, by default it is 2, to save bandwidth. The maximal possible value is 9, but this is rarely useful. | |
| May 17, 2023 at 16:26 | comment | added | Notamathematician | Thank you for answer! Is it correct that FindStat automatically finds the desired sequence of transformations? Is it also correct that you set the length of transformations by yourself? If so, how do you know what the length should be? Also, could you look at this question: mathoverflow.net/questions/436336/…? | |
| May 17, 2023 at 16:22 | comment | added | Martin Rubey | Indeed, the map can be simplified as follows: it is the binary word corresponding to the minimal elements of the increasing runs of the permutation which are not right-to-left maxima. This is immediate from the description of findstat.org/MapsDatabase/Mp00235 | |
| May 17, 2023 at 14:52 | comment | added | Martin Rubey | Note that the statistic is defined for all permutations, even those that do not avoid $1-23-4$. I think that this makes it even more likely that the map simplifies, I did not check. | |
| May 17, 2023 at 14:43 | history | answered | Martin Rubey | CC BY-SA 4.0 |