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arXiv · 2608.01497

Square roots in the Appell group and Sprugnoli arrays

Paul Barry
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Abstract

We introduce a special mapping from pairs of power series to the group of Sprugnoli matrices. This mapping has the property when the second argument is an even power series, then the square of the resulting Sprugnoli array is an aerated element of the Appell subgroup of the Riordan group. This allows us to explore the square roots of elements in the aerated Appell subgroup. As the identity is an element of this subgroup, we are led to explore related involutions in the Sprugnoli group.

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Paul Barry. 2026-08-02. Square roots in the Appell group and Sprugnoli arrays. https://arxiv.org/abs/2608.01497

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