On a generalization of the method of boundary functionals

The method of boundary functionals was suggested by A. A. Sapozhenko for solving a series of enumeration problems. In this paper, we extend the method to the case of functional pairs with characteristic three and obtain an asymptotic formula for the sum of boundary functionals over regular families of subsets.
This research was supported by the Russian Foundation for Basic Research, grant 04–01–00359.