Timeline for Lengths of cycles in non-crossing partitions
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2020 at 0:58 | comment | added | Richard Stanley | I don't know how to do this more refined problem. | |
| Dec 12, 2020 at 20:15 | comment | added | combinatorix_curious | @Richard Stanley, thank you very much for your comment. I am actually interested in something more. You gave the number of permutations $𝑔$ with $𝑚_𝑖$ such that $𝜂^{−1}𝑔$ has the maximum number of cycles. I would like to know how many of these permutations $𝑔$ with $𝑚_𝑖$ have $𝜂^{−1}𝑔$ with $\tilde{m}_𝑖$? | |
| Dec 6, 2020 at 16:54 | comment | added | Richard Stanley | If you just want the number of permutations $g$ with $m_i$ $i$-cycles such that $\eta^{-1}g$ has the maximum number of cycles, then you are enumerating noncrossing partitions with $m_i$ $i$-element blocks. This was done by Kreweras. The number is $n(n-1)\cdots(n-k+2)/m_1!m_2!\cdots m_n!$, where $k=\sum m_i$ (the total number of blocks). See e.g. equation (3) of core.ac.uk/download/pdf/82503989.pdf. | |
| Dec 5, 2020 at 23:10 | review | First posts | |||
| Dec 6, 2020 at 3:41 | |||||
| Dec 5, 2020 at 23:07 | history | asked | combinatorix_curious | CC BY-SA 4.0 |