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DEGREE OF THE
$W$-OPERATOR AND NONCROSSING PARTITIONS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 23 October 2019, pp. 186-200
- Print publication:
- April 2020
-
- Article
- Export citation
-
The
$W$-operator, 
$W([n])$, generalises the cut-and-join operator. We prove that 
$W([n])$ can be written as the sum of 
$n!$ terms, each term corresponding uniquely to a permutation in 
$S_{\!n}$. We also prove that there is a correspondence between the terms of 
$W([n])$ with maximal degree and noncrossing partitions.
