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An involution on Dyck paths in the region $\defc\le\min(\area,\dinv)$ that interchanges area and dinv
We construct an explicit involution on Dyck paths satisfying $\defc\le\min(\area,\dinv)$ that interchanges area and dinv. The construction relies on a number of new combinatorial objects developed here and two main external tools: the dual Dyck insertion of \cite{Hawkes26} and the Garsia--Milne invo
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