1 citations · 1 across the 5 of their papers we have counts for
6 papers
Quantizations of Continued Fractions
A. Muhammed Uludağ, Esra Ünal Yilmaz
We introduce a four-parameter deformation of continued fractions, which we call -deformation. We study some particular cases and compare them with the q-deformation of continu…
The conumerator
A. Muhammed Uludağ, Buket Eren Gökmen
In this paper, we answer the question: "what is the qth Fibonacci number, where q is a positive rational?". The answer is the codenominator function, which is an integral-valued ma…
Testing the transcendence conjectures of a modular involution of the real line and its continued fraction statistics
Hakan Ayral, A. Muhammed Uludağ
We study the values of the recently introduced involution J (jimm) of the real line, which is equivariant with the action of the group PGL(2,Z). We test our conjecture that this in…
Mapping class groupoids and Thompson's groups
A. Muhammed Uludağ, Mustafa Topkara, Özge Ülkem +1
We introduce a groupoid ${\mathbf{ΠMG}}}$, called the fundamental modular groupoid, which is a variant of Penner's mapping class groupoid. We study how it relates to the surface ma…
On the involution of the real line induced by Dyer's outer automorphism of PGL(2,Z)
A. Muhammed Uludağ, Hakan Ayral
We study the involution of the real line induced by the outer automorphism of the extended modular group PGL(2,Z). This `modular' involution is discontinuous at rationals but satis…
Fundamental Groups of a Class of Rational Cuspidal Plane Curves
A. Muhammed Uludağ
We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. W…