Crossings and nestings in set partitions of classical types
The electronic journal of combinatorics, Tome 17 (2010)
In this article, we investigate bijections on various classes of set partitions of classical types that preserve openers and closers. On the one hand we present bijections for types $B$ and $C$ that interchange crossings and nestings, which generalize a construction by Kasraoui and Zeng for type $A$. On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the cardinality of a maximal crossing with the cardinality of a maximal nesting, as given by Chen, Deng, Du, Stanley and Yan for type $A$. For type $D$, we were only able to construct a bijection between non-crossing and non-nesting set partitions. For all classical types we show that the set of openers and the set of closers determine a non-crossing or non-nesting set partition essentially uniquely.
@article{10_37236_392,
author = {Martin Rubey and Christian Stump},
title = {Crossings and nestings in set partitions of classical types},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/392},
zbl = {1277.05011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/392/}
}
Martin Rubey; Christian Stump. Crossings and nestings in set partitions of classical types. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/392
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