Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4599356 | Linear Algebra and its Applications | 2014 | 11 Pages |
Abstract
Let T=[tn,k]n,kâ¥0 be an infinite lower triangular matrix defined byt0,0=1,tn+1,0=âj=0nzjtn,j,tn+1,k+1=âj=knaj,ktn,j for n,kâ¥0, where all zj,aj,k are nonnegative and aj,k=0 unless jâ¥kâ¥0. We show that the sequence (tn,0)nâ¥0 is log-convex if the coefficient matrix [ζ,A] is TP2, where ζ=[z0,z1,z2,â¦]â² and A=[ai,j]i,jâ¥0. This gives a unified proof of the log-convexity of many well-known combinatorial sequences, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the Schröder numbers, the Bell numbers, and so on.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yi Wang, Zhi-Hai Zhang,