Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2015-04-15

Journal: LINEAR ALGEBRA AND ITS APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 471

Page Number: 383-393

ISSN: 0024-3795

Key Words: Totally positive matrix; Recursive matrix; Tridiagonal matrix

Abstract: 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.