Total positivity of recursive matrices

Xi Chen, Huyile Liang, Yi Wang
2015 Linear Algebra and its Applications  
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_ka_n,k-1+s_ka_n,k+t_k+1a_n,k+1, where a_n,k=0 unless n> k> 0 and r_k,s_k,t_k are all nonnegative. 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
more » ... ications we give the total positivity of the above mentioned combinatorial triangles in a unified approach.
doi:10.1016/j.laa.2015.01.009 fatcat:rrhxsfavo5cn7pqzuliw2zfu7a