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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\u2019s 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\u2019s alternating scheme domains belong to this family of domains while single-crossing domains do not.<\/jats:p>","DOI":"10.1007\/s00355-024-01520-7","type":"journal-article","created":{"date-parts":[[2024,4,3]],"date-time":"2024-04-03T12:02:17Z","timestamp":1712145737000},"page":"57-67","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A family of condorcet domains that are single-peaked on a circle"],"prefix":"10.1007","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0397-6290","authenticated-orcid":false,"given":"Arkadii","family":"Slinko","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,3]]},"reference":[{"key":"1520_CR1","volume-title":"The theory of committees and elections","author":"D Black","year":"1958","unstructured":"Black D (1958) The theory of committees and elections. 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