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LOG-CONCAVITY OF ROWS OF PASCAL TYPE TRIANGLES
Tekijät: Foldes Stephan, Major László
Kustantaja: UTIL MATH PUBL INC
Julkaisuvuosi: 2020
Journal: Utilitas Mathematica
Tietokannassa oleva lehden nimi: UTILITAS MATHEMATICA
Lehden akronyymi: UTILITAS MATHEMATICA
Vuosikerta: 116
Aloitussivu: 203
Lopetussivu: 210
Sivujen määrä: 8
ISSN: 0315-3681
Verkko-osoite: http://www.combinatorialmath.ca/Utilitas/
Tiivistelmä
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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