Abstract
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.
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The authors would like to thank George Andrews, Paweł Hitczenko and Anatoly Vershik for their wonderful insights and helpful comments.
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Part of this research was conducted, while the authors were graduate students at Drexel University. Some of the work on this project was funded under European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 335220.
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Dalal, A.J., Lohss, A. & Parry, D. Statistical Structure of Concave Compositions. Ann. Comb. 25, 729–756 (2021). https://doi.org/10.1007/s00026-021-00543-6
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DOI: https://doi.org/10.1007/s00026-021-00543-6