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DEGREE OF THE
$W$-OPERATOR AND NONCROSSING PARTITIONS
Published online by Cambridge University Press: 23 October 2019
Abstract
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.
MSC classification
- Type
- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.