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We establish the unimodality and the asymptotic strong unimodality of theordinary multinomials and give their smallest mode leading to the expression ofthe maximal probability of convolution powers of the discrete uniformdistribution. We conclude giving the generating functions of the sequence ofgeneralized ordinary multinomials and for an extension of the sequence ofmaximal probabilities for convolution power of discrete uniform distribution.

Unimodality of ordinary multinomials and maximal probabilities of convolution powers of discrete uniform distribution