A Unified Approach for the Catalan Matrices by Using Riordan Arrays

Tian-Xiao He, Yan-Ni Dong, Sheng-liang Yang, Yan-Xue Xu

Research output: Journal ArticleArticlepeer-review


We study generalized Catalan matrices based on the Riordan array and Fuss–Catalan numbers. A unified combinatorial interpretation for the entries of the generalized Catalan matrices is presented by means of m-Dyck paths. Some properties and examples of the generalized Catalan matrices are given including a new convolution formula for the generalized Catalan numbers. Finally, we present applications of generalized Catalan matrices to the problems in counting the hill-free and lower peak-free m-Dyck paths.
Original languageAmerican English
JournalLinear Algebra and Its Applications
StatePublished - Dec 2018


  • Physical Sciences and Mathematics
  • Mathematics

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