Generalized Schröder Matrices Arising from Enumeration of Lattice Paths

Tian-Xiao He, Sheng-liang Yang, Lin Yang

Research output: Journal ArticleArticlepeer-review


We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps E = (1, 0), D = (1, 1), N = (0, 1), and D ′ = (1, 2) and not going above the line y = x . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition, we find some new interesting identities.
Original languageAmerican English
JournalCzechoslovak Mathematical Journal
Volume70 (145)
StatePublished - Dec 5 2019


  • Riordan array
  • lattice path
  • Delannoy matrix
  • Schröder number
  • Schröder matrix


  • Applied Mathematics
  • Mathematics

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