This paper defines the multiple Riordan group and characterizes multiple Riordan arrays through A-sequences and Z-sequences.
This is the first paper of a sequence papers on the multiple Riordan group and the multiple Riordon type arrays. We give a comprehensive discussion of the multiple Riordan arrays and characterize them by an A-sequence and multiple Z-sequences. The multiple Riordan group and some of its subgroups are defined. In addition, we give compressions of multiple Riordan arrays and their sequence characterizations. The total positivity of the compressions of multiple Riordan arrays is studied.
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Tian-Xiao He (2025) studied this question.