2 papers
math.CO2025
A Simple Recursive Relation Characterizes a Tree Associated to Generalized Farey Sequences
Makoto Nagata, Yoshinori Takei
This paper proves that two differently defined rooted binary trees are isomorphic. The first tree is one associated to a version of Farey sequences where the vertices correspond to…
math.CO2024
A congruential recurrence characterizes the inverses of Sós permutations
Makoto Nagata, Yoshinori Takei
In a proof of the three gaps theorem, a class of permutations known as the Sós permutations was introduced. It is known that a Sós permutation, as a sequence, satisfies a certain…