Opened 7 years ago
Last modified 5 years ago
#14127 new enhancement
class for rook boards (Young shapes, diagram of a permutation)
Reported by: | ahmorales | Owned by: | ahmorales |
---|---|---|---|
Priority: | trivial | Milestone: | sage-6.4 |
Component: | combinatorics | Keywords: | days45, rook placement, Rothe diagram, Young diagram, Le diagram |
Cc: | Merged in: | ||
Authors: | ahmorales | Reviewers: | chrisjamesberg |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Add a class for a Board (subset of entries in [0,1,..,r-1] x [0,1,...,s-1] ). Examples are
- Straight shape
- Skew shape
- Diagram of a permutation
- Hulls of permutations
And procedures to generate:
- placements of non-attacking rooks
- Le diagrams.
References
- Richard Stanley, Enumerative Combinatorics, Volume 1, 2nd Edition, Ch. 2.3
- Laurent Manivel, Symmetric Functions, Schubert polynomials and Degeneraci Loci, Ch. 2.
- Sjostrand, J. Bruhat intervals as rooks on skew Ferrers boards, J. Combin. Theory Ser. A, 2007, 114, 7, 1182-1198
Change History (5)
comment:1 Changed 7 years ago by
comment:2 Changed 6 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:3 Changed 6 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:4 Changed 5 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:5 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
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You should make sure to provide an interface to
simplicial_complexes.ChessboardComplex(r,s)
: yourBoard
class could have asimplicial_complex
method (or something similar) which returns the complex. Actually, you could do this:The point behind having a
_simplicial_
method is that ifB
is an instance of theBoard
class, you can then callSimplicialComplex(B)
and it will call this method.You also might be able to improve the implementation of the
ChessboardComplex
or thematching
function in the same file, and that would be greatly appreciated.Edit: I guess the
_simplicial_
method would be more appropriate on the class of allBoards
, not for a single board. Anyway...