Added a method to compute the Tutte Symmetric function of a graph #38677
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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. Analogous to the Stanley's tree isomorphism conjecture, determining graph classes that are distinguished by their Tutte symmetric function is actively investigated. |
src/sage/graphs/graph.py
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| ret = m.zero() | ||
| V = self.vertices() | ||
| E = list(self.edges(labels=False)) | ||
| M = Counter(E) |
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Here you can certainly do directly M = Counter(self.edge_iterator(labels=False)), thus avoiding intermediate variable E which is not used elsewhere.
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This is not changed in what I can see.
src/sage/graphs/graph.py
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| ret = m.zero() | ||
| V = self.vertices() | ||
| E = list(self.edges(labels=False)) | ||
| M = Counter(E) |
There was a problem hiding this comment.
This is not changed in what I can see.
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@tscrim, do you know why the CI is not running for this PR ? it would be useful to finalize the review. I think the code is ok now. |
because the author is a first time contributor. |
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Documentation preview for this PR (built with commit cb6624d; changes) is ready! 🎉 |
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What's the purpose of this last commit ? why is method |
A conflict was raised highlighting |
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Methods |
| from sage.combinat.sf.sf import SymmetricFunctions | ||
| from sage.combinat.set_partition import SetPartitions | ||
| from sage.misc.misc_c import prod | ||
| from sage.arith.misc import factorial |
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you don't need to import factorial anymore
| m = SymmetricFunctions(R).m() | ||
| ret = m.zero() | ||
| V = self.vertices() | ||
| M = Counter(list(self.edges(labels=False))) |
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Does this really need to get the list of edges? I thought having an iterator is sufficient.In particular, this does not match @dcoudert 's suggestion.
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
⌛ Dependencies
No pending dependencies
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"