Andrews, George E. Concave compositions. (English) Zbl 1229.05029 Electron. J. Comb. 18, No. 2, Research Paper P6, 13 p. (2011). Summary: Concave compositions are compositions (i.e., ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function discoveries also lead to new facts about concatenatable, spiral, self-avoiding walks. Cited in 1 ReviewCited in 25 Documents MSC: 05A17 Combinatorial aspects of partitions of integers PDFBibTeX XMLCite \textit{G. E. Andrews}, Electron. J. Comb. 18, No. 2, Research Paper P6, 13 p. (2011; Zbl 1229.05029) Full Text: EuDML EMIS