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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_21136_CMJ_2019_0348_18,
     author = {Yang, Lin and Yang, Sheng-Liang and He, Tian-Xiao},
     title = {Generalized {Schr\"oder} matrices arising from enumeration of lattice paths},
     journal = {Czechoslovak Mathematical Journal},
     pages = {411--433},
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2020},
     doi = {10.21136/CMJ.2019.0348-18},
     mrnumber = {4111851},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0348-18/}
}
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
SP  - 411
EP  - 433
VL  - 70
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0348-18/
DO  - 10.21136/CMJ.2019.0348-18
LA  - en
ID  - 10_21136_CMJ_2019_0348_18
ER  - 
%0 Journal Article
%A Yang, Lin
%A Yang, Sheng-Liang
%A He, Tian-Xiao
%T Generalized Schröder matrices arising from enumeration of lattice paths
%J Czechoslovak Mathematical Journal
%D 2020
%P 411-433
%V 70
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0348-18/
%R 10.21136/CMJ.2019.0348-18
%G en
%F 10_21136_CMJ_2019_0348_18
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

Cité par Sources :