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Danilov, Vladimir I.; Karzanov, Alexander V.; Koshevoy, Gleb A.
Discrete Applied Mathematics, 03/2021, Letnik: 292Journal Article
We deal with the problem of aggregation of rhombus tilings with the help of a certain natural majority rule. As a 2-dimensional counterpart of the well-known problem of aggregation of linear orders and related Condorcet domains, in this paper we introduce a Condorcet super-domain to be a collection of rhombus tilings on a zonogon Z(n;2) satisfying the property that whenever the voting designs (ballots) belong to this collection, then the majority rule produces a rhombus tiling as well. A study of Condorcet super-domains and methods of constructing them form the main subject of this paper.
