LOG-CONCAVITY OF ROWS OF PASCAL TYPE TRIANGLES

: Foldes Stephan, Major László

Publisher: UTIL MATH PUBL INC

: 2020

Utilitas Mathematica

: UTILITAS MATHEMATICA

: 116

: 203

: 210

: 8

: 0315-3681

: http://www.combinatorialmath.ca/Utilitas/

Menon's proof of the preservation of log-concavity of sequences 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 convolution 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.