The rotation group of Rubik's cube. - Oliver Knill; Roman Maeder (SIGSAM Bull., 1987)

Diagonalization of Abel's Integral Operator. - Oliver Knill (SIAM J. Appl. Math., 1994)

Complexity Growth in Almost Periodic Fluids in the Case of Lattice Gas Cellular Automata and Vlasov Systems. - Oliver Knill; Evan Reed (Complex Syst., 1996)

A structure from motion inequality - Oliver Knill; Jose Ramirez-Herran (CoRR, 2007)

On Ullman's theorem in computer vision - Oliver Knill; Jose Ramirez-Herran (CoRR, 2007)

Space and camera path reconstruction for omni-directional vision - Oliver Knill; Jose Ramirez-Herran (CoRR, 2007)

A graph theoretical Gauss-Bonnet-Chern Theorem - Oliver Knill (CoRR, 2011)

On the Dimension and Euler characteristic of random graphs - Oliver Knill (CoRR, 2011)

A graph theoretical Poincare-Hopf Theorem - Oliver Knill (CoRR, 2012)

The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory - Oliver Knill (CoRR, 2012)

On index expectation and curvature for networks - Oliver Knill (CoRR, 2012)

An index formula for simple graphs - Oliver Knill (CoRR, 2012)

A Brouwer fixed point theorem for graph endomorphisms - Oliver Knill (CoRR, 2012)

The Lusternik-Schnirelmann theorem for graphs - Frank Josellis; Oliver Knill (CoRR, 2012)

The Dirac operator of a graph. - Oliver Knill (CoRR, 2013)

The Euler characteristic of an even-dimensional graph. - Oliver Knill (CoRR, 2013)

Counting rooted forests in a network. - Oliver Knill (CoRR, 2013)

On quadratic orbital networks. - Oliver Knill (CoRR, 2013)

The zeta function for circular graphs. - Oliver Knill (CoRR, 2013)

The McKean-Singer Formula in Graph Theory - Oliver Knill (CoRR, 2013)

Thinking like Archimedes with a 3D printer - Oliver Knill; Elizabeth Slavkovsky (CoRR, 2013)

A notion of graph homeomorphism. - Oliver Knill (CoRR, 2014)

Classical mathematical structures within topological graph theory. - Oliver Knill (CoRR, 2014)

If Archimedes would have known functions. - Oliver Knill (CoRR, 2014)

Characteristic Length and Clustering. - Oliver Knill (CoRR, 2014)

Curvature from Graph Colorings. - Oliver Knill (CoRR, 2014)

Coloring graphs using topology. - Oliver Knill (CoRR, 2014)

Graphs with Eulerian unit spheres. - Oliver Knill (CoRR, 2015)

The Kuenneth formula for graphs. - Oliver Knill (CoRR, 2015)

The Jordan-Brouwer theorem for graphs. - Oliver Knill (CoRR, 2015)

The graph spectrum of barycentric refinements. - Oliver Knill (CoRR, 2015)

A Sard theorem for graph theory. - Oliver Knill (CoRR, 2015)

Universality for Barycentric subdivision. - Oliver Knill (CoRR, 2015)

Gauss-Bonnet for multi-linear valuations. - Oliver Knill (CoRR, 2016)

Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes. - Oliver Knill (CoRR, 2016)

Some experiments in number theory. - Oliver Knill (CoRR, 2016)

On Fredholm determinants in topology. - Oliver Knill (CoRR, 2016)

Sphere geometry and invariants. - Oliver Knill (CoRR, 2017)

On Helmholtz free energy for finite abstract simplicial complexes. - Oliver Knill (CoRR, 2017)

On a Dehn-Sommerville functional for simplicial complexes. - Oliver Knill (CoRR, 2017)

On the arithmetic of graphs. - Oliver Knill (CoRR, 2017)

The strong ring of simplicial complexes. - Oliver Knill (CoRR, 2017)

On Atiyah-Singer and Atiyah-Bott for finite abstract simplicial complexes. - Oliver Knill (CoRR, 2017)

One can hear the Euler characteristic of a simplicial complex. - Oliver Knill (CoRR, 2017)

An Elementary Dyadic Riemann Hypothesis. - Oliver Knill (CoRR, 2018)

Listening to the cohomology of graphs. - Oliver Knill (CoRR, 2018)

The hydrogen identity for Laplacians. - Oliver Knill (CoRR, 2018)

The Cohomology for Wu Characteristics. - Oliver Knill (CoRR, 2018)

Combinatorial manifolds are Hamiltonian. - Oliver Knill (CoRR, 2018)

Eulerian edge refinements, geodesics, billiards and sphere coloring. - Oliver Knill (CoRR, 2018)

Cartan's Magic Formula for Simplicial Complexes. - Oliver Knill (CoRR, 2018)

A Reeb sphere theorem in graph theory. - Oliver Knill (CoRR, 2019)

The average simplex cardinality of a finite abstract simplicial complex. - Oliver Knill (CoRR, 2019)

Dehn-Sommerville from Gauss-Bonnet. - Oliver Knill (CoRR, 2019)

More on Numbers and Graphs. - Oliver Knill (CoRR, 2019)

A parametrized Poincare-Hopf Theorem and Clique Cardinalities of graphs. - Oliver Knill (CoRR, 2019)

The energy of a simplicial complex. - Oliver Knill (CoRR, 2019)

Energized simplicial complexes. - Oliver Knill (CoRR, 2019)

A simple sphere theorem for graphs. - Oliver Knill (CoRR, 2019)

Poincare Hopf for vector fields on graphs. - Oliver Knill (CoRR, 2019)

More on Poincare-Hopf and Gauss-Bonnet. - Oliver Knill (CoRR, 2019)

Constant index expectation curvature for graphs or Riemannian manifolds. - Oliver Knill (CoRR, 2019)

Green functions of Energized complexes. - Oliver Knill (CoRR, 2020)

Complexes, Graphs, Homotopy, Products and Shannon Capacity. - Oliver Knill (CoRR, 2020)

Graph complements of circular graphs. - Oliver Knill (CoRR, 2021)

Remarks about the Arithmetic of Graphs. - Oliver Knill (CoRR, 2021)

Shannon capacity, Chess, DNA and Umbrellas. - Oliver Knill (CoRR, 2021)

Analytic torsion for graphs. - Oliver Knill (CoRR, 2022)

Eigenvalue bounds of the Kirchhoff Laplacian. - Oliver Knill (CoRR, 2022)

The Tree-Forest Ratio. - Oliver Knill (CoRR, 2022)

The Babylonian Graph. - Oliver Knill (CoRR, 2022)

The Sphere Formula. - Oliver Knill (CoRR, 2023)

Characteristic Topological Invariants. - Oliver Knill (CoRR, 2023)

Spectral monotonicity of the Hodge Laplacian. - Oliver Knill (CoRR, 2023)

Cohomology of open sets. - Oliver Knill (CoRR, 2023)

The Three Tree Theorem. - Oliver Knill (CoRR, 2023)

Arboricity and Acyclic Chromatic Number. - Oliver Knill (CoRR, 2023)

Discrete Algebraic sets in Discrete Manifolds. - Oliver Knill (CoRR, 2023)

Manifolds from Partitions. - Oliver Knill (CoRR, 2024)

Morse and Lusternik-Schnirelmann for graphs. - Oliver Knill (CoRR, 2024)

On Symmetries of Finite Geometries. - Oliver Knill (CoRR, 2024)

Soft Barycentric Refinement. - Oliver Knill (CoRR, 2025)

Interacting Geodesics on Discrete Manifolds. - Oliver Knill (CoRR, 2025)