Row Sums and Alternating Sums of Riordan Arrays

Tian-Xiao He, Louis W. Shapiro

Research output: Journal ArticleArticlepeer-review


Here we use row sum generating functions and alternating sum generating functions to characterize Riordan arrays and subgroups of the Riordan group. Numerous applications and examples are presented which include the construction of Girard-Waring type identities. We also show the extensions to weighted sum (generating) functions,
called the expected value (generating) functions of Riordan arrays.
Original languageAmerican English
JournalLinear Algebra and Its Applications
StatePublished - 2016


  • Riordan arrays
  • Riordan group
  • Appell subgroup
  • asso- ciate subgroup
  • Bell subgroup
  • derivative subgroup
  • checkerboard subgroup
  • hitting- time subgroup
  • Girard-Waring type identities
  • sum functions of Riordan arrays


  • Mathematics

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