Koshelev, V. N.; Stasevich, S. I. Enumeration of events on plane lattices. (English. Russian original) Zbl 0956.05008 Dokl. Math. 58, No. 2, 257-259 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 362, No. 5, 595-597 (1998). From the text: The problem of enumeration of events that occur on an integer lattice whose edges are binary variables that interact through a common node is considered. The interaction is defined by the list of admissible binary configurations formed by the edges emanating from a node, and the problem of enumeration consists in the representation of the number of occurring events (the realizations of the lattice) as a function of the dimensions and the topology of the lattice and the type of interaction between edges. On a one-dimensional lattice, the problem reduces to the enumeration of realizations of the corresponding Markov chain and is easily solved by applying an appropriate matrix method. For two-dimensional lattices, the problem becomes substantially more complicated, and its solution, as a rule, is closely related to a specific model of interaction. The matrix method developed below that essentially employs the matrix description of the two-dimensional-lattice topology seems to be more universal. We analyze lattices of three modifications: a rectangular lattice on a plane, a rectangular diagonally oriented lattice on a cylinder, and a lattice on a cylinder with the honeycomb topology. MSC: 05A15 Exact enumeration problems, generating functions Keywords:enumeration of events; configurations; lattice; Markov chain; rectangular lattice on a plane; rectangular diagonally oriented lattice on a cylinder; lattice on a cylinder with the honeycomb topology PDFBibTeX XMLCite \textit{V. N. Koshelev} and \textit{S. I. Stasevich}, Dokl. Math. 58, No. 2, 595--597 (1998; Zbl 0956.05008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 362, No. 5, 595--597 (1998)