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A bijection for switching all crossing and nesting numbers for a subclass of matchings, set partitions, and permutations

Filed under:
Lily Yen (Capilano University and Simon Fraser University, Canada), 19 July 2012, 1:30 p.m., RISC seminar room
When Jul 19, 2012
from 01:30 PM to 03:00 PM
Where RISC seminar room
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A bijection for switching all crossing and nesting numbers for a subclass of matchings, set partitions, and permutations

For a subclass of matchings, set partitions, and permutations, we describe a direct bijection involving only arc annotated diagrams that not only interchanges maximum nesting and crossing numbers, but also all refinements of crossing and nesting numbers. Furthermore, we show that the bijection cannot be extended to a larger class of arc annotated diagrams.