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FlagSOS

A julia package for extremal combinatorics based on the flag algebra method.

https://github.com/danielbrosch/flagsos.jl

Science Score: 44.0%

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    Found CITATION.cff file
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    Low similarity (8.8%) to scientific vocabulary
Last synced: 6 months ago · JSON representation ·

Repository

A julia package for extremal combinatorics based on the flag algebra method.

Basic Info
Statistics
  • Stars: 2
  • Watchers: 1
  • Forks: 0
  • Open Issues: 4
  • Releases: 3
Created over 2 years ago · Last pushed 7 months ago
Metadata Files
Readme License Citation

README.md

FlagSOS.jl

Stable Dev Build Status Coverage Aqua

A julia package for extremal combinatorics based on the flag algebra method and its variants. The package offers various hierarchies to compute lower bounds for problems of the form

$$ \begin{aligned} \infM\enspace & F(M)\ \text{s.t. }& Gi(M) \geq 0 \quad\text{ for }i=1,\dots,k,\ & H_i(M) = 0 \quad\text{ for }i = 1,\dots, \ell, \end{aligned} $$

where $F$, $Gi$, $Hi$ are quantum flags (linear combinations of sub-model density functions), and $M$ is a model of fixed size or a converging sequence in a given theory. The constraints can include labels, but then the entire $S_n$ orbit needs to be included.

Check out the documentation for details.

Citing

See CITATION.bib for the relevant reference(s).

Owner

  • Name: Daniel Brosch
  • Login: DanielBrosch
  • Kind: user
  • Company: Tilburg University

PhD-candidate at Tilburg University. Mostly focused on symmetric semidefinite and polynomial optimization. Currently working on flag sums-of-squares.

Citation (CITATION.bib) 

@phdthesis{Brosch2022,
  abstract  = {This dissertation explores different approaches to and applications of symmetry reduction in convex optimization. Using tools from semidefinite programming, representation theory and algebraic combinatorics, hard combinatorial problems are solved or bounded. The first chapters consider the Jordan reduction method, extend the method to optimization over the doubly nonnegative cone, and apply it to quadratic assignment problems and energy minimization on a discrete torus. The following chapter uses symmetry reduction as a proving tool, to approach a problem from queuing theory with redundancy scheduling. The final chapters propose generalizations and reductions of flag algebras, a powerful tool for problems coming from extremal combinatorics.},
  author    = {Daniel Brosch},
  doi       = {10.26116/12v4-k024},
  isbn      = {978 90 5668 690 1},
  language  = {English},
  publisher = {CentER, Center for Economic Research},
  school    = {Tilburg University},
  series    = {CentER Dissertation Series},
  title     = {Symmetry reduction in convex optimization with applications in combinatorics},
  year      = {2022}
}

GitHub Events

Total
  • Watch event: 1
  • Delete event: 1
  • Push event: 40
  • Pull request event: 8
  • Create event: 6
Last Year
  • Watch event: 1
  • Delete event: 1
  • Push event: 40
  • Pull request event: 8
  • Create event: 6

Packages

  • Total packages: 1
  • Total downloads:
    • julia 1 total
  • Total dependent packages: 0
  • Total dependent repositories: 0
  • Total versions: 3
juliahub.com: FlagSOS

A julia package for extremal combinatorics based on the flag algebra method.

  • Versions: 3
  • Dependent Packages: 0
  • Dependent Repositories: 0
  • Downloads: 1 Total
Rankings
Dependent repos count: 10.1%
Dependent packages count: 37.0%
Average: 43.7%
Forks count: 53.6%
Stargazers count: 74.2%
Last synced: 6 months ago

Dependencies

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