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math.CO2026
Square roots in the Appell group and Sprugnoli arrays
Paul Barry
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 t…
math.CO2026
Pascal-like Sprugnoli arrays
Paul Barry
In this note, we look at the structure and properties of palindromic or Pascal-like Sprugnoli arrays. We show that there are two closely related families of these arrays. We give c…
math.CO2026
A new group in the Riordan family of matrix groups: the Sprugnoli group
Paul Barry
We define a group of lower-triangular matrices whose columns are defined by power series. This group can be seen as a generalization of the (ordinary) Riordan group and the double…