A family of condorcet domains that are single-peaked on a circle
证明了广义Fishburn域是最大Condorcet域，并给出新组合解释，表明这些域在圆上单峰，经典单峰域、单谷域和Fishburn交替方案域属于该族，但单交叉域不属于。
Abstract 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 that all of them are single-peaked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domain remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn’s domains which provide a constructive proof of single-peakedness of these domains on a circle. We show that classical single-peaked domains and single-dipped domains as well as Fishburn’s alternating scheme domains belong to this family of domains while single-crossing domains do not.