The Multiple Riordan Group and the Multiple Riordan Type Arrays

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.