Article
Generalized Schröder Matrices Arising from Enumeration of Lattice Paths
Czechoslovak Mathematical Journal
(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.
Keywords
- Riordan array,
- lattice path,
- Delannoy matrix,
- Schröder number,
- Schröder matrix
Disciplines
Publication Date
Winter December 5, 2019
DOI
10.21136/CMJ.2019.0348-18
Publisher Statement
Czechoslovak Mathematical Journal is published jointly by Springer and the Institute of Mathematics of the Academy of Sciences of the Czech Republic. For more information on this journal please visit Springer.
Citation Information
Tian-Xiao He, Sheng-liang Yang and Lin Yang. "Generalized Schröder Matrices Arising from Enumeration of Lattice Paths" Czechoslovak Mathematical Journal Vol. 70 (145) Iss. 2 (2019) p. 411 - 433 ISSN: 0011-4642 Available at: http://works.bepress.com/tian_xiao_he/98/