  Enumeration of quarter-plane lattice walks with small steps is a classical
problem in combinatorics. An effective approach is the kernel method and the
solution is derived by positive term extraction. Another approach is to reduce
the lattice walk problem to a Carleman type Riemann boundary value problem
(RBVP) and solve it by complex analysis. There are two parameter characterizing
the solutions of a Carleman type Riemann Boundary value problem, the index
$\chi$ and the conformal gluing function $w(x)$. In this paper, we propose a
combinatorial insight to the RBVP approach. We show that the index can be
treated as the canonical factorization in the kernel method and the conformal
gluing function can be turned into a conformal mapping such that after this
mapping, the positive degree terms and the negative degree terms can be
naturally separated. The combinatorial insight of RBVP provide a connection
between the kernel method, the RBVP approach and the Tutte's invariant method.
