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论文类型：期刊论文

发表时间：2019-08-01

发表刊物：DISCRETE MATHEMATICS

收录刊物：SCIE

卷号：342

期号：8

页面范围：2270-2277

ISSN号：0012-365X

关键字：Delannoy number; Delannoy triangle; Delannoy polynomial; Polynomial with only real zeros; Asymptotically normal distribution

摘要：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.