Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics

We present q-Stirlingʹs formula, q-multinomial coefficient, one-to-one correspondence between q-multinominal coefficient and Tsallis entropy, q-Pascalʹs triangle and a conjecture on the q-central limit theorem in Tsallis statistics for the generalization of the well-known fundamental formulas to systems exhibiting power-law behaviors. The main approach is based on the q-product, uniquely determined by Tsallis entropy, which has already been successfully applied to our recent proof of the law of error in Tsallis statistics.