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

Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ

“…The q-product, q-factorial and q-ratio are applied to the definition of the q-multinomial coefficient [8].…”

“…Based on these fundamental formulas, we obtain the one-to-one correspondence (2) between the q-multinomial coefficient and Tsallis entropy as follows [8].…”

“…Moreover, when ν = 2 − q and ν = 1/q, each interpretation of the (µ, ν, q)-relation shown in (8) and (10) is respectively presented. The final section is devoted to our conclusion.…”

“…For all many applications of the MaxEnt for Tsallis entropy (1), there have been missing a combinatorial consideration in Tsallis statistics until recently [8], whose ideas originate from…”

“…By means of the qproduct uniquely determined by the q-exponential function [11][12] as the q-exponential law, the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy is obtained as follows [8]: for n = k i=1 n i and n i ∈ N if q = 2,…”