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digital cash and blind signiture

My question is about the basics of the topic "creating digital cash". At the very beginning of that topic the amount of the banknote and a serial number are the requirements for generating a signature to avoid pirate copy of the banknote. That implies that the bank can trace the banknote and their customers by the serial number. To anonymize the tracing there comes a method called blind signature. My question is about the coherence between the serial number and signature for that banknote. How can the bank generate a signature for a banknote without notice the serial number and at the same time to hold the coherence between signature and serial number?