Geodesic
Geometric aspects of a~deformation of the standard addition on integer lattices
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 231-240

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Let $\mathfrak A_n$ be the set of all those vectors of the standard lattice $\mathbb Z^n$ whose coordinates are pairwise incomparable modulo $n$. In this paper, we analyze the group structure on $\mathfrak A_n$ that arises from the construction of a deformation of multiplication described by V. M. Buchstaber. We present a geometric realization of this group in the ambient space $\mathbb R^n\supset\mathbb Z^n$ and find its generators and relations. 
@article{TM_2014_286_a10,
     author = {S. Yu. Tsarev},
     title = {Geometric aspects of a~deformation of the standard addition on integer lattices},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {231--240},
     publisher = {mathdoc},
     volume = {286},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_286_a10/}
}
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S. Yu. Tsarev. Geometric aspects of a~deformation of the standard addition on integer lattices. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, convex polytopes, and related topics, Tome 286 (2014), pp. 231-240. http://geodesic.mathdoc.fr/item/TM_2014_286_a10/