Statistical structure of concave compositions

2 May 2016  ·  Avinash J. Dalal, Amanda Lohss, Daniel Parry ·

In this paper, we study concave compositions, an extension of partitions that were considered by Andrews, Rhoades, and Zwegers. They presented several open problems regarding the statistical structure of concave compositions including the distribution of the perimeter and tilt, the number of summands, and the shape of the graph of a typical concave composition... We present solutions to these problems by applying Fristedt's conditioning device on the uniform measure. read more

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Combinatorics Number Theory Probability 05A16, 60C05, 11P82