Generalized Schröder matrices arising from enumeration of lattice paths

Lin Yang; Sheng-Liang Yang; Tian-Xiao He

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 411-433
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Yang, Lin, Yang, Sheng-Liang, and He, Tian-Xiao. "Generalized Schröder matrices arising from enumeration of lattice paths." Czechoslovak Mathematical Journal 70.2 (2020): 411-433. <http://eudml.org/doc/297124>.

@article{Yang2020,
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^\{\prime \} = (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.},
author = {Yang, Lin, Yang, Sheng-Liang, He, Tian-Xiao},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riordan array; lattice path; Delannoy matrix; Schröder number; Schröder matrix},
language = {eng},
number = {2},
pages = {411-433},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized Schröder matrices arising from enumeration of lattice paths},
url = {http://eudml.org/doc/297124},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Yang, Lin
AU - Yang, Sheng-Liang
AU - He, Tian-Xiao
TI - Generalized Schröder matrices arising from enumeration of lattice paths
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 411
EP - 433
AB - 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^{\prime } = (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.
LA - eng
KW - Riordan array; lattice path; Delannoy matrix; Schröder number; Schröder matrix
UR - http://eudml.org/doc/297124
ER -

References

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