Geodesic
Generalized Schröder matrices arising from enumeration of lattice paths
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 411-433.

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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.
DOI : 10.21136/CMJ.2019.0348-18
Classification : 05A15, 05A19, 11B83, 15A24
Keywords: Riordan array; lattice path; Delannoy matrix; Schröder number; Schröder matrix 
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     title = {Generalized {Schr\"oder} matrices arising from enumeration of lattice paths},
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     publisher = {mathdoc},
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Yang, Lin; Yang, Sheng-Liang; He, Tian-Xiao. Generalized Schröder matrices arising from enumeration of lattice paths. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 411-433. doi : 10.21136/CMJ.2019.0348-18. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0348-18/

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