Inductive and injective proofs of log concavity results (Q1111553)

A necessary condition is obtained for every row of a triangular array to be log concave, where a sequence \(\{a_ k\}_{0\leq k\leq n}\) is called log concave if \(a_{k-1}a_{k+1}\leq a^ 2_ k,\) for all k, \(0<k<n\). This result is used to inductively construct injections showing the log concavity of the binomial coefficients and Stirling numbers of both kinds. These proofs are related to graphical interpretation of these numbers by Wilf.