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Tamari intervals and blossoming trees
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Abstract
We introduce a simple bijection between Tamari intervals and the blossoming trees (Poulalhon and Schaeffer, 2006) encoding planar triangulations, using a new meandering representation of such trees. Its specializations to the families of synchronized, Kreweras, new/modern, and infinitely modern intervals give a combinatorial proof of the counting formula for each family. Compared to (Bernardi and Bonichon, 2009), our bijection behaves well with the duality of Tamari intervals, also enabling the counting of self-dual intervals.
Mathematics Subject Classifications: 05A15, 05A19
Keywords: Tamari intervals, blossoming trees, enumeration, duality
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