LOG-CONCAVITY OF ROWS OF PASCAL TYPE TRIANGLES

Abstract

Menon's proof of the preservation of log-concavity of se¬quences under convolution becomes simpler when adapted to 2-sided infinite sequences. Under assumption of log-concavity of two 2-sided infinite sequences, the existence of the convolution Is characterised by a convergence criterion. Preservation of log-concavity under con¬volution yields another method of establishing the log-concavity of rows of certain Pascal type triangles. This includes in particular the log-concavity of rows of a weighted Delannoy triangle. The method is also compared with known techniques of proving log-concavity. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.