Pascal-like Matrix And Related Sequences

Total positivity of matrix is one of the primary topics in matrix theory, it sets up con-nections between unimodality, log-concavity, log-convexity, Polya frequecy sequence and Stieltjes moment sequence. Pascal-like matrix is a classical research object in combina-torics. The main job of this paper is to study the total positivity, Polya frequecy sequence and Stieltjes moment sequence of Pascal-like matrix, which may be summarized as follows.In the first chapter, we introduced some basic concepts and background about total positivity. Polya frequecy sequence, Stieltjes moment sequence. Pascal-like matrix, etc.In the second chapter, we gave an algebraic proof of the total positivity of (xn,yn, zn, t) Pascal-like matrix by transformation which preserves total positivity.In the third chapter, we provided a simple proof of the total positivity of (x,y,z) Pascal-like matrix by LDU decomposition, and study the Polya frequecy sequences, Stielt-jes moment sequences in (x, y, z) Pascal-like matrix.