A new formalism of the bi-adjoint scalar $\ell$-loop planar integrand recursion

In this paper, we proposed a new method to obtain $\ell$-loop planar integrands of bi-adjoint scalars. From the equation of motion, we defined comb components and then constructed loop kernels. We constructed the $\ell$-loop planar integrands using these objects by some recursion rules. Finally, we raised a new formalism of the recursion, which is more elegant than the traditional one, based on the "graded inverse variables".