Geodesic
On the entropy of a~multinomial distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 196-198

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It is shown that the multinomial distribution corresponding to $n$ independent trials with probabilities $p_0,\dots,p_{t+1}$ of $t+1$ outcomes in each trial, has the maximal entropy if $p_0=\dots=p_t=1/(1+t)$. 
@article{TVP_1978_23_1_a19,
     author = {P. Mateev},
     title = {On the entropy of a~multinomial distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {196--198},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a19/}
}
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P. Mateev. On the entropy of a~multinomial distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 1, pp. 196-198. http://geodesic.mathdoc.fr/item/TVP_1978_23_1_a19/