Related Work

Igor and I were recently informed of work by Jean-Louis Nicolas which contains a proof of the log-concavity of the partition numbers:

Sur les entiers N pour lesquels il y a beaucoup de groupes abéliens d’ordre N,
Annales de l’institut Fourier, tome 28, no 4 (1978), p. 1-16.

http://www.numdam.org/item?id=AIF_1978__28_4_1_0
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