Journal of Integer Sequences, Vol. 22 (2019), Article 19.2.8

On the Unimodality of Convolutions of Sequences of Binomial Coefficients

Tricia Muldoon Brown
Department of Mathematical Sciences
Georgia Southern University
11935 Abercorn Street
Savannah, GA 31419


We provide necessary and sufficient conditions on the unimodality of a convolution of two sequences of binomial coefficients preceded by a finite number of ones. These convolution sequences arise as rank sequences of posets of vertex-induced subtrees for a particular class of trees. The number of such trees whose poset of vertex-induced subgraphs containing the root is not rank unimodal is determined for a fixed number of vertices i.

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(Concerned with sequences A002620 A005993 A024206 A080232 A320657.)

Received October 23 2018; revised versions received November 8 2018; April 23 2019. Published in Journal of Integer Sequences, May 6 2019.

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