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Non-associative Hopf Algebra on Dyck Paths Arising from the Shuffle-insertion Product
In this paper, we define a shuffle-insertion product and a cut-box coproduct on the vector space spanned by Dyck paths, where the product is commutative but non-associative. We prove that the product and coproduct are compatible, making the space a non-associative bialgebra. This bialgebra is connec
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