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Indexed by:Journal Papers

Date of Publication:2019-08-01

Journal:DISCRETE MATHEMATICS

Included Journals:SCIE

Volume:342

Issue:8

Page Number:2270-2277

ISSN No.:0012-365X

Key Words:Delannoy number; Delannoy triangle; Delannoy polynomial; Polynomial with only real zeros; Asymptotically normal distribution

Abstract:The Delannoy numbers d(n, k) count the number of lattice paths from (0, 0) to (n-k, k) using steps (1, 0), (0, 1) and (1, 1). We show that the zeros of all Delannoy polynomials d(n)(x) = E-k=0(n) d(n, k)x(k) are in the open interval (-3 -2 root 2, -3 + 2 root 2) and are dense in the corresponding closed interval. We also show that the Delannoy numbers d(n, k) are asymptotically normal (by central and local limit theorems). (C) 2019 Elsevier B.V. All rights reserved.