Entropies of the partitions of the unit interval generated by the Farey tree

Chromatic Numbers of Suborbital Graphs for the Modular Group and the Extended Modular Group

“…The following remark includes some facts of the fractions and their mediants used to construct the vertex set of the Farey tree. Its edges will not be mentioned in this paper; see more in [5][6][7] about the Farey tree. We are now ready to talk more about the vertex set of the Farey tree.…”

Moments for the multidimensional Mönkemeyer algorithm

“…The partitions (1) and the corresponding moments (2) are related to investigations devoted to the dynamics generated by the Farey map [7] and also [5,9]. Also in (2), an asymptotic formula for the moments was proved; this formula was refined later in [13].…”

О Разбиении Отрезка $[0,1]$, Порожденном Последовательностями Броко

“…В работе [5] Н. Г. Мощевитин и A. Жиглявский рассматривали поведение σ(F n ) при n стремящемся к бесконечности. Там было доказано следующее асимптотическое равенство.…”

“…Отметим, что история вопроса и обзор близких результатов имеются во введении упомянутой ранее работы [5]. § 2.…”