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| We prove that given an affine IFS on the real line and a probability vector then there exists a corresponding combinatorial identity associated with binomial coefficients and moment sequence with respect to the invariant measure $mu$ of the IFS. In particular, when $mu$ is the restriction of Lebesgue measure to a close interval, we obtain some well-known or unknown combinatorial identities. |
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| Keywords:combinatorial identities, iterated function systems, binomial coefficient, invariant measure, Lebesgue measure |
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