Estakhr Permutation Amplitude, (String Theory)

Permutation $P(n,m)=\frac{n!}{(n- m)!}$, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality. The formula is the following: $P(\frac{1}{2}(k_1+k_2)^2-2,\frac {-1}{2}(k_2+k_3)^2+1)P(\frac{1}{2} (k_2+k_3)^2-2,\frac{1}{2} (k_2+k_3)^2-2)$, k$^{n}$ is a vector (such as a four- vector) referring to the momentum of the n$^{th}$ particle. relashionship between Euler beta function and Permutation: $B(n,m)=P(n-1,-m)P(m-1,m-1)$, Relationship between the Veneziano amplitude and Estakhr Permutation Amplitude: $B(\frac{1}{2}(k_1+k_2)^2-1,\frac {1}{2}(k_2+k_3)^2-1)=P(\frac{1}{2} (k_1+k_2)^2-2,\frac{-1}{2} (k_2+k_3)^2+1)P(\frac{1}{2} (k_2+k_3)^2-2,\frac{1}{2} (k_2+k_3)^2-2)$, (The notion of permutation relates to act of permuting or rearranging members of a set into a particular sequence or order)