14 citations · 46 across the 15 of their papers we have counts for
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A hidden Condorcet domain in Loday's realisation of the associahedron
Arkadii Slinko
We prove that Loday's polytopal realisation of the nth Tamari lattice T_n, called associahedron, has 2^{n-1} common points with the permutohedron, which form a maximal never-middle…
A composition of Condorcet domains
Dominic Keehan, Arkadii Slinko
Inspecting known maximal Condorcet domains on 4 variables classified by Tobias Dittrich we find that 9 out of 18 of them are created using a certain composition of smaller domains.…
A combinatorial representation of Arrow's single-peaked domains
Arkadii Slinko
The most studied class of Condorcet domains (acyclic sets of linear orders) is the class of peak-pit domains of maximal width. It has a number of combinatorial representations by s…
A family of Condorcet domains that are single-peaked on a circle
Arkadii Slinko
Fishburn's alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving…
Generalisation of the Danilov-Karzanov-Koshevoy Construction for Peak-Pit Condorcet Domains
Arkadii Slinko
Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting operation of composition on tiling Condorcet domains and using it they disproved a long-standing probl…
Hierarchical Simple Games: Representations and Weightedness
Tatiana Gvozdeva, Ali Hameed, Arkadii Slinko
In many situations, both in human and artificial societies, cooperating agents have different status with respect to the activity and it is not uncommon that certain actions are on…