It is shown that there are ( 2n-r-1 n-r) noncrossing partitions of an n-set together with a distinguished block of size r, and ( n k-1)( n-r-1 k-2) of these have k blocks, generalizing a result of Bóna on partitions with one crossing. Furthermore, specializing natural q-analogues of these formulae with q equal to certain d th roots-of-unity gives the number of such objects having d-fold rotational symmetry.
|Original language||English (US)|
|Number of pages||5|
|State||Published - Apr 1 2011|
- Cyclic sieving phenonomenon
- Noncrossing partition