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The solution of the T-t fundamental combinatorial problem is given in a purely analytic form as a sum over binomials. This simplifies other calculations considerably. For an illustration the moments of the optical absorption line shape in the strong coupling limit are derived in a closed form. Furtheron, the optical zero phonon line is calculated. An application to a T - t phase transition chain is indicated.

The T-t Jahn-Teller System: Solution of the Fundamental Combinatorial Problem and its Application to Moments and Zero Phonon Line