The method of boundary functionals for irregular structures

The method of boundary functionals suggested by A. A. Sapozhenko who applied it to a series of enumeration problems is successfully employed in the case of partially ordered sets with regular structure of the strata, for example, on the unit $n$-dimensional cube $B^n$. But partially ordered sets occurring in some problems, say, the three-valued $n$-dimensional lattice $E^n_3$, do not possess a regular structure. In this paper, the method of boundary functionals is extended to the case of such sets and is used to find the asymptotic behaviour of the number of antichains in the three central strata of $E^n_3$.
This research was supported by the Russian Foundation for Basic Research, grant 01–01–00266.