  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-picked 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.
