Mike Winkler, Ph.D.

collaborators

5 papers

math.GM2026

Realized Rank Certificates for Matchstick Frameworks and Insertion Edges

Mike Winkler

We give an exact, checkable rank-certificate method for realized planar unit-distance frameworks. The method is motivated by Vogel's computations for matchstick graphs and by the i…

math.GM2026

Thinned Wallis-type prime products in residue classes modulo $2^{m}$

Mike Winkler

For odd primes $p$ we consider the factors $A (p) = (p - I ¨ _{4} (p)) / (p + I ¨ _{4} (p))$ , where $I ¨ _{4}$ is the quadratic Dirichlet character modulo $4$ , and study products of $A (p)$ restricted to…

math.GM2026

Deterministic Structures in the Stopping Time Dynamics of the 3x+1 Problem

Mike Winkler

The $3 x + 1$ problem concerns the iteration of the map $T : Z \to Z$ defined by $T (x) = x /2$ for even $x$ and $T (x) = (3 x + 1) /2$ for odd $x$ . We study the coefficient stoppi…

math.CO2026

On the existence of 4-regular matchstick graphs

Mike Winkler, Peter Dinkelacker, Stefan Vogel

A matchstick graph is a planar unit-distance graph. We call it \emph{4-regular} if every vertex has degree 4. While examples of 4-regular matchstick graphs with fewer than 63 verti…

math.GM2026

An Identity of Fillipi Related to Fermat-Type Equations

Mike Winkler, Andreas Fillipi

We give a structural proof of an algebraic identity proposed by Fillipi in 2014. For every integer $n \geq 2$ , the identity represents an explicit multiple of $x^{n} + y^{n} - z^{n}$ as $\mathc…

Realized Rank Certificates for Matchstick Frameworks and Insertion Edges

Thinned Wallis-type prime products in residue classes modulo 2m

Deterministic Structures in the Stopping Time Dynamics of the 3x+1 Problem

On the existence of 4-regular matchstick graphs

An Identity of Fillipi Related to Fermat-Type Equations

Thinned Wallis-type prime products in residue classes modulo $2^{m}$