### Abstract

We consider weighted large and small Schröder paths with up steps (1,1), down steps (1,-1) assigned the weight of 1 and with level steps (2,0) assigned the weight of t, where t is a real number. The weight of a path is the product of the weights of all its steps. Let rℓ(t) and sℓ(t) be the total weight of all weighted large and small Schröder paths from (0,0) to (2ℓ,0), respectively. For constants α, β, we derive the generating functions and the explicit formulae for the determinants of the Hankel matrices (αri+j-2(t)+βri+j-1(t))i,j=1n, (αri+j-1(t) +βri+j(t))i,j=1n, (αsi+j-2(t)+βsi+j-1(t))i,j=1n and (αsi+j-1(t)+βsi+j(t))i,j=1n combinatorially via suitable lattice path models.

Original language | English |
---|---|

Pages (from-to) | 2285-2299 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 437 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2012 Nov 1 |

### Fingerprint

### Keywords

- Combinatorial methods
- Hankel determinants
- Non-intersecting lattice paths
- Schröder numbers

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

*Linear Algebra and Its Applications*,

*437*(9), 2285-2299. https://doi.org/10.1016/j.laa.2012.05.024