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      Log-concavity of rows of Pascal type triangles

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          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 a method of establishing the log-concavity of rows of a large class of Pascal type triangles, including a weighted generalization of the Delannoy triangle. This method is also compared with known techniques of proving log-concavity.

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          On the convolution of logarithmically concave sequences

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            Generalizing the Combinatorics of Binomial Coefficients via -Nomials

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              Author and article information

              Journal
              2016-08-14
              Article
              1608.04126
              ce683479-8936-4047-b540-14f83adca295

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              Custom metadata
              Primary 05A15, 40A05, Secondary 11B83
              math.CO

              Combinatorics
              Combinatorics

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