#18050: Implement dual equivalence graphs
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: dual equivalence | Merged in:
graphs | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 274a0187d4382d8fd24bf6a72f0b54bb5a64b580
public/crystals/dual_equivalence-18050| Stopgaps:
Dependencies: |
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Comment (by mantepse):
I think the docstring of `Partition.dual_equivalence_graph` could be
clearer. I suggest
{{{
Two permutations `p` and `q` differ by an elementary dual Knuth
relation (of color `i`), when, in one line notation, the letter
`i` does not occur between `i-1` and `i+1`, and `q` is obtained
from `p` by switching the places of `i-1` and `i+1`.
Two standard Young tableaux of shape `\lambda` differ by an
elementary dual Knuth relation (of color `i`), if their content
reading words differ by an elementary dual Knuth relation (of
color `i`).
The *dual equivalence graph* is the edge-colored graph formed by
the set of standard Young tableaux of shape `\lambda` where edges
colored by `i` are given by dual equivalences of color `i`.
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/18050#comment:12>
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