Geodesic
The arithmetic and geometry of one-dimensional quasilattices
Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 255-262

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In the paper we use some methods of number theory to study arithmetic and geometric properties of one-dimensional quasilattices. The parametrization of any quasilattice is obtained. Conditions of combinatorial and geometrical equivalence of quasilattices are found. We also study solutions of linear diophantine equations over quasilattices. 
@article{CHEB_2010_11_1_a26,
     author = {A. V. Shutov},
     title = {The arithmetic and geometry of one-dimensional quasilattices},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {255--262},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a26/}
}
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A. V. Shutov. The arithmetic and geometry of one-dimensional quasilattices. Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 255-262. http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a26/