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Added a method to compute the Tutte Symmetric function of a graph #38677

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Added a method that returns the Tutte symmetric function of the graph. Added references accordingly.

Tutte symmetric function of a graph

For a graph G (may contain multiedges and loops), the new methods returns the Tutte symmetric function of the graph. It is implemented by using the expansion of the Tutte symmetric function in the monomial symmetric function basis.
The references are added and the index.rst file is updated accordingly.

The Tutte symmetric function of a graph is a chromatic invariant that generalizes the Tutte polynomial to a symmetric function. One can recover the chromatic symmetric function of a graph from its Tutte symmetric function. Analogous to the Stanley's tree isomorphism conjecture, the graph classes distinguished by their Tutte symmetric function are actively investigated.
The newly added method returns the monomial symmetric function expansion of the Tutte symmetric function of a graph.

📝 Checklist

  • The title is concise and informative.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation and checked the documentation preview.

⌛ Dependencies

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Comment:

All tests are passed. However, unable to run docbuild. Shows the following error:
"File "", line 198, in _run_module_as_main
File "", line 88, in _run_code"

@sagar-math sagar-math marked this pull request as draft September 19, 2024 06:15
@sagar-math sagar-math marked this pull request as ready for review September 19, 2024 06:17
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For a graph G, its Tutte symmetric function is a chromatic invariant that generalizes the Tutte polynomial to a symmetric function.
We add a method to compute the Tutte symmetric function of a graph using its expansion in the augmented monomial symmetric function basis.

Analogous to the Stanley's tree isomorphism conjecture, determining graph classes that are distinguished by their Tutte symmetric function is actively investigated.

@tscrim @amritanshu-prasad @mantepse

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@dcoudert dcoudert left a comment

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further improvements are certainly possible.

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2 participants