Skip to content
  • About quantum calculus
  • Graph geometry
  • SingleVariable
    • Pecha Kucha
    • Math 1a
  • Multi Variable
  • Search
Quantum Calculus
Calculus without limits
 
  • About quantum calculus
  • Graph geometry
  • SingleVariable
    • Pecha Kucha
    • Math 1a
  • Multi Variable
  • Search
Category: <span>graph geometry</span>
Home quantum calculus Archive for category "graph geometry"

Category: graph geometry

Graph Complements of Cyclic Graphs
discrete geometry, graph geometry, Graph theory

Graph Complements of Cyclic Graphs

By oliverknill January 18, 2021 January 21, 2021  cyclic graphs

Graph complements of cylic graphs are homotopic to spheres or wedge sums of spheres. Their unit spheres are graph complements of path graphs and have Gauss-Bonnet curvature which converges to a limit.

Go to the post"Graph Complements of Cyclic Graphs"
Shannon Capacity
discrete geometry, graph geometry, Graph theory

Shannon Capacity

By oliverknill December 8, 2020 December 14, 2020  Connection graph, Shannon cacacity

The Shannon capacity of a connection graph is computed.

Go to the post"Shannon Capacity"
Mickey Mouse Sphere Theorem
discrete geometry, graph geometry, Graph theory

Mickey Mouse Sphere Theorem

By oliverknill October 11, 2019 October 17, 2019  Curvature, graphs, Mickey mouse, mickey mouse sphere theorem, sphere theorem

The Mickey mouse theorem assures that a connected positive curvature graph of positive dimension is a sphere.

Go to the post"Mickey Mouse Sphere Theorem"
Poincare-Hopf and the Clique Problem
graph geometry, Graph theory

Poincare-Hopf and the Clique Problem

By oliverknill June 21, 2019 June 21, 2019  poincare hopf

The parametrized poincare-hopf theorem allows to see the f-vector of a graph in terms of the f-vector s of parts of the unit spheres of the graph.

Go to the post"Poincare-Hopf and the Clique Problem"
Euler Game
discrete geometry, graph geometry, Graph theory

Euler Game

By oliverknill August 19, 2018 August 23, 2018  discrete billiard, discrete geodesic flow, Edge refinement

We prove that any discrete surface has an Eulerian edge refinement. For a 2-disk, an Eulerian edge refinement is possible if and only if the boundary length is divisible by 3

Go to the post"Euler Game"
Helmholtz free energy for simplicial complexes
graph geometry, Graph theory, quantum calculus

Helmholtz free energy for simplicial complexes

By oliverknill March 19, 2017 June 5, 2017  entropy

Over spring break, the Helmholtz paper [PDF] has finished. (Posted now on “On Helmholtz free energy for finite abstract simplicial complexes”.) As I will have little time … ….

Go to the post"Helmholtz free energy for simplicial complexes"
Sphere Spectrum
graph geometry, Graph theory

Sphere Spectrum

By oliverknill January 5, 2017 January 14, 2017

This is a research in progress note while finding a proof of a conjecture formulated in the unimodularity theorem paper.

Go to the post"Sphere Spectrum"
The unimodularity theorem proof
graph geometry

The unimodularity theorem proof

By oliverknill December 24, 2016 January 21, 2018

The proof of the unimodularity theorem is finished.

Go to the post"The unimodularity theorem proof"
Euler and Fredholm
graph geometry, Graph theory

Euler and Fredholm

By oliverknill December 1, 2016 December 26, 2016  fredholm determinant, prime graph, unimodularity theorem

The following picture illustrates the Euler and Fredholm theme in the special case of the prime graphs introduced in the Counting and Cohomology paper. The story there … ….

Go to the post"Euler and Fredholm"
Back to Top
LoginPersonal Website HarvardTwitterYoutubeLinkedin
©2019 Quantum Calculus
Powered by Fluida & WordPress.