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We study the new relation [1] between the anomalous dimensions, resummedthrough next-to-next-to-leading-logarithmic order, in theDokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the firstMellin moments D_{q,g}(\mu^2) of the fragmentation functions, which correspondto the average multiplicities of hadrons in jets initiated by quarks andgluons, respectively. This relation is shown to lead to probabilisticproperties of the properly rescaled parton jet multiplicities obtained fromstandard ones by extracting the quark and gluon "color charges" C_F and C_A,respectively.

SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution