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论文类型：期刊论文

发表时间：2015-04-15

发表刊物：LINEAR ALGEBRA AND ITS APPLICATIONS

收录刊物：SCIE、EI、Scopus

卷号：471

页面范围：383-393

ISSN号：0024-3795

关键字：Totally positive matrix; Recursive matrix; Tridiagonal matrix

摘要：Let A = [a(n),(k)](n,k >= 0) be an infinite lower triangular matrix defined by the recurrence
   a(0,0) = 1, a(n+1,k) = r(k)a(n,k-1) + S(k)a(n,k) + t(k+1)a(n,k+1),
   where a(n,k) = 0 unless n >= k >= 0 and r(k), s(k), t(k) are all non-negative. Many well-known combinatorial triangles are such matrices, including the Pascal triangle, the Stirling triangle (of the second kind), the Bell triangle, the Catalan triangles of Aigner and Shapiro. We present some sufficient conditions such that the recursive matrix A is totally positive. As applications we give the total positivity of the above mentioned combinatorial triangles in a unified approach. (C) 2015 Elsevier Inc. All rights reserved.