DEGREE OF THE -OPERATOR AND NONCROSSING PARTITIONS
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DEGREE OF THE -OPERATOR AND NONCROSSING PARTITIONS
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.
- Sun Yat-sen University China (People's Republic of)
Permutations, words, matrices, \(W\)-operator, Symmetric functions and generalizations, cut-and-join operator, Partitions of sets, Representations of group algebras, permutation, noncrossing partition
Permutations, words, matrices, \(W\)-operator, Symmetric functions and generalizations, cut-and-join operator, Partitions of sets, Representations of group algebras, permutation, noncrossing partition
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selected citations
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These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
Citations provided by BIP!popularityPopularity provided by BIP!
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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