Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 411-433, 2020
Generalized Schröder matrices arising from enumeration of lattice paths
Lin Yang, Sheng-Liang Yang, Tian-Xiao He
Received July 26, 2018. Published online December 5, 2019.
Abstract: 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.
Affiliations: Lin Yang, Sheng-Liang Yang (corresponding author), Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, Gansu, P. R. China, e-mail: email@example.com, firstname.lastname@example.org; Tian-Xiao He, Department of Mathematics, Illinois Wesleyan University, Bloomington, IL, 61702-2900, USA, e-mail: email@example.com