ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS-Reference-Cited by-同舟云学术

ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS

Published:2012-02 Issue:01 Volume:08 Page:175-188
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

NOBLE ROB¹

Affiliation:

1. Department of Mathematics and Statistics, Dalhousie University, Chase Building, Halifax, NS, B3H 3J5, Canada

Abstract

The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic coefficients that lie in a number field. In this paper we apply a generalization of a method of Stoll and Haible to obtain divisibility properties for the asymptotic coefficients in this case. We also provide a similar result for a special case of the diagonal with slope 2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042112500108

Reference10 articles.

1. Why Delannoy numbers?

2. Advanced Combinatorics

3. Analytic Combinatorics

4. Weighted lattice paths

5. On weighted lattice paths

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