title: Structures on lattices: some useful relations.
abstract: We consider a lattice and structures on it generated by a set of configurations of a cluster. Using some general considerations, we show that there exist linear relations between fractional contents of these configurations in the structures. Such relations can be useful for the determination of the ground states of lattice-gas models (or equivalent spin models). As an illustration we consider a set of configurations of a seven-site cluster on the triangular lattice.
authors.affiliation: Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine. dubl@ph.icmp.lviv.ua
authors.forename: Yu I
authors.initials: YI
authors.lastname: Dublenych