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论文类型：期刊论文

发表时间：2020-12-01

发表刊物：DISCRETE MATHEMATICS

卷号：343

期号：12

ISSN号：0012-365X

关键字：Motzkin number; Total positivity; Polynomial with only real roots; Asymptotic normality; Riordan array

摘要：The Motzkin numbers count the number of lattice paths which go from (0, 0) to (n, 0) using steps (1, 1), (1, 0) and (1,-1) and never go below the x-axis. Let M-n,M-k be the number of such paths with exactly k horizontal steps. We investigate the analytic properties of various combinatorial triangles related to the Motzkin triangle [M-n,M-k](n,k >= 0), including their total positivity, the real-rootedness and interlacing property of the generating functions of their rows, and the asymptotic normality (by central and local limit theorems) of these triangles. We also prove several identities related to these triangles. (c) 2020 Elsevier B.V. All rights reserved.