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Statistics for unimodal sequences 1 1 Introduction and Statement of results 1 2 Preliminaries 8 2.1 Notation 8 2.2 Euler--Maclaurin summation, logarithmic series, and integral calculations 9 2.3 Saddle-point method 10 2.4 Probability theory 12 3 Boltzmann models for partitions and the work of Fristedt 12 4 Conditioned Boltzmann model 13 5 Proofs of the main results 26 5.1 Small parts: the proofs of Theorem 1.5, Corollary 1.6, and Theorem 1.11 27 5.2 Large parts: the proofs of Theorems 1.4 and 1.10 29 5.3 Total small parts: proof of Theorem 1.8 31 6 Moment generating functions 33 References 36

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