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T.V. Andreeva

The method of boundary functionals for non-regular 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 Bⁿ. But partially ordered sets occurring in some problems, say, the three-valued n-dimensional lattice , 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 .

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 14, 01/2004
Pages: 13 - 32

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