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Full-Text Articles in Applied Mathematics
Four Named To Endowed Professorships, Kim Hill
Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He
Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He
Scholarship
Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schroder numbers and small Schroder numbers, respectively. Using the characterization sequences of Bell-type Riordan arrays, some properties and expressions including the Taylor expansions of generalized Catalan numbers are given. A few combinatorial interpretations of the generalized Catalan numbers are also provided. Finally, a generalized Motzkin numbers …
Mathematics Professor’S Publications Add Up, Kim Hill
Mathematics Professor’S Publications Add Up, Kim Hill
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