Mike Winkler, Ph.D.

activity

20142026

most citedOn the existence of 4-regular matchstick graphs

3 citations · 8 across the 14 of their papers we have counts for

collaborators

Showing math.GMShow all

9 papers · 1 filter

math.GM2026

Admissible $q x + 1$ Sequences, Semiconvergents, and Rational Catalan Numbers

Mike Winkler

Let $q \geq 3$ be odd and put $m_{r} = ⌊ r lo g_{2} q ⌋$ . We count parity sequences with exactly $r$ odd entries for which the coefficient in the $q x + 1$ iteration first drops belo…

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 $A (p) = (p - χ_{4} (p)) / (p + χ_{4} (p))$ , where $χ_{4}$ is the quadratic Dirichlet character modulo $4$ , and study products of $A (p)$ restricted to uni…

math.GM2021

Aperiodic Sets of Prototiles Extracted From the Penrose Rhomb Tiling

Mike Winkler

We present aperiodic sets of prototiles whose shapes are based on the well-known Penrose rhomb tiling. Some decorated prototiles lead to an exact Penrose rhomb tiling without any m…

math.GM2019

Approximate Solutions of 4-regular Matchstick Graphs with 50-62 Vertices

Mike Winkler

A 4-regular matchstick graph is a planar unit-distance graph whose vertices have all degree 4. Examples of 4-regular matchstick graphs are currently known for all number of vertice…

math.GM2017

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.GM2015★ 2 cited

New results on the stopping time behaviour of the Collatz 3x + 1 function

Mike Winkler

Let $σ_{n} = ⌊ 1 + n \cdot lo g_{2} 3 ⌋$ . For the Collatz 3x + 1 function exists for each $n \in N$ a set of different residue classes $(mod 2^{σ_{n}})$ of starting num…

math.GM2014★ 1 cited

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…

math.GM2014

Fibonacci Enumeration of Residue Classes via Forbidden Binary Factors

Mike Winkler

Binary words avoiding adjacent ones are counted by Fibonacci numbers. We identify a natural residue-class enumeration in which this classical word count arises from parity data of…

Admissible qx+1 Sequences, Semiconvergents, and Rational Catalan Numbers

Realized Rank Certificates for Matchstick Frameworks and Insertion Edges

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

Aperiodic Sets of Prototiles Extracted From the Penrose Rhomb Tiling

Approximate Solutions of 4-regular Matchstick Graphs with 50-62 Vertices

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

New results on the stopping time behaviour of the Collatz 3x + 1 function

An Identity of Fillipi Related to Fermat-Type Equations

Fibonacci Enumeration of Residue Classes via Forbidden Binary Factors

Admissible $q x + 1$ Sequences, Semiconvergents, and Rational Catalan Numbers

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