3 papers
math.NT2025
Superoptimal continued fractions
Slade Sanderson
Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of…
math.DS2025
A unifying theory for metrical results on regular continued fraction convergents and mediants
Karma Dajani, Cor Kraaikamp, Slade Sanderson
We revisit Ito's (\cite{I1989}) natural extension of the Farey tent map, which generates all regular continued fraction convergents and mediants of a given irrational. With a sligh…
math.NT2025
Inducing contractions of the mother of all continued fractions
Karma Dajani, Cor Kraaikamp, Slade Sanderson
We introduce a new, large class of continued fraction algorithms producing what are called contracted Farey expansions. These algorithms are defined by coupling two acceleration te…