4 papers
math.AT2025
Finite Topological Space Filtrations: A Topological Framework for Data Analysis
Selçuk Kayacan
We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construct a sequence of coarsening topologies o…
math.GR2025
Subrack lattices of finite solvable and metacyclic groups
Selçuk Kayacan
A group with conjugation operation is a rack. We call such racks \emph{group racks}. In this paper we study finite group racks via their subrack lattices. Heckenberger, Sharesh…
cs.CR2025
Presentations of Racks
Selçuk Kayacan
Presentations of racks is studied and a cryptographic protocol defined on racks is proposed.
math.GR2024
Subrack Lattices of Conjugation Racks
Selçuk Kayacan
A rack is a set with a binary operation such that left multiplications are automorphisms of the set and a quandle is a rack satisfying a certain condition. Let be a subset of a…