Generalized Schröder matrix and its combinatorial interpretation

Abstract

In the present article, we introduce a new family of matrices that generalizes the Schröder matrices of the first and the second kind, then we show that these matrices are connected to inverse generalized Delannoy matrices. We also give a combinatorial interpretation of these new matrices by using a family of weighted lattice paths whose step set is ; with the additional property that the paths do not fall below the line , and the last step of the paths are not horizontal.

Keywords:

• Riordan array
• lattice path
• Delannoy matrix
• Schröder matrix

AMS Subject Classifications:

• 15A09
• 05A05
• 05A15

Acknowledgements

The authors thank the anonymous referee for his/her comments which helped to improve the article.

Notes

No potential conflict of interest was reported by the authors.

1 Many integer sequences and their properties are expounded on The On-Line Encyclopaedia of Integer Sequences [24].