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Symmetric Maximal Condorcet Domains
Order. 2023. Vol. 40. No. 2. P. 289–309.
Karpov A., Slinko A.
We introduce the operation of composition of domains and show that it reduces the classification of symmetric maximal Condorcet domains to the indecomposable ones. The only non-trivial indecomposable symmetric maximal domains known are the domains consisting of four linear orders examples of which were given by Raynaud (1981) and Danilov and Koshevoy (Order 30(1), 181–194 2013). We call them Raynaud domains and we classify them in terms of simple permutations, a well-researched combinatorial object. We hypothesise that no other indecomposable symmetric maximal domains exist.
Publication based on the results of:
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
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n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
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Alexander Karpov, Slinko A., Theory and Decision 2023 Vol. 94 No. 1 P. 97–120
We present a new method of constructing Condorcet domains from pairs of Condorcet domains of smaller sizes (concatenation + shuffle scheme). The concatenation + shuffle scheme provides maximal, connected, copious, peak-pit domains whenever the original domains have these properties. It allows to construct maximal peak-pit Condorcet domains that are larger than those obtained by the Fishburn’s alternating scheme for ...
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