  Earlier in the study of the combinatorial properties of the heat kernel of
Laplace operator with covariant derivative diagram technique and matrix
formalism were constructed. In particular, this formalism allows you to control
the coefficients of the heat kernel, which is useful for calculations. In this
paper, a simple case is considered with abelian connection in two-dimensional
space. This model allows us to give a mathematical description of operators and
find relation between operators and generating functions of numbers.
