A1 Refereed original research article in a scientific journal
LOG-CONCAVITY OF ROWS OF PASCAL TYPE TRIANGLES
Authors: Foldes Stephan, Major László
Publisher: UTIL MATH PUBL INC
Publication year: 2020
Journal: Utilitas Mathematica
Journal name in source: UTILITAS MATHEMATICA
Journal acronym: UTILITAS MATHEMATICA
Volume: 116
First page : 203
Last page: 210
Number of pages: 8
ISSN: 0315-3681
Web address : http://www.combinatorialmath.ca/Utilitas/
Abstract
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.
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.
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