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Consider a rowwise independent triangular array of gamma random variableswith varying parameters. Under several different conditions on the shapeparameter, we show that the sequence of row-maximums converges weakly afterlinear or power transformation. Depending on the parameter combinations, weobtain both Gumbel and non-Gumbel limits.  The weak limits for maximum of the coordinates of certain Dirichlet vectorsof increasing dimension are also obtained using the gamma representation.

Maxima of Dirichlet and triangular arrays of gamma variables