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.
Full version: pdf,
(Concerned with sequences
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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