Implement a bijection between Knutson-Tao puzzles and LR tableaux #39581
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The previous implementation iterated over sets, which caused inconsistent output; this was solved by adding 'UniqueRepresentation' as a parent for one class and by sorting outputs in many doctests. The new code iterates over tuples.
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Documentation preview for this PR (built with commit 112b035; changes) is ready! 🎉 |
src/sage/combinat/partition.py
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| def abacus_to_partition(abacus): | ||
| r""" | ||
| Returns a partition from an abacus. |
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First line should use "imperative mode", so "Return" and not "Returns"
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also we prefer long but explicit names for functions and methods, without acronyms inside |
So would you for instance call the method |
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yes, please do |
src/sage/combinat/partition.py
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| part = [] | ||
| n = len(abacus) | ||
| k = 0 | ||
| for i in range(0,n): |
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| for i in range(0,n): | |
| for i in range(n): |
| k += 1 | ||
| part.insert(0, i+1-k) | ||
| elif abacus[i] != '0' and abacus[i] != 0: | ||
| raise ValueError('an abacus should be a tuple, list or string of 0s and 1s') |
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there should be a doctest for the raise (with a bad input provoking the error)
src/sage/combinat/skew_tableau.py
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| False | ||
| sage: SkewTableau([[None,1],[2,2]]).is_littlewood_richardson() | ||
| False | ||
src/sage/combinat/skew_tableau.py
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| 1/\0 0\/1 | ||
| sage: ''.join(puzzle.south_labels()) | ||
| '01000010001001000000' | ||
| sage: # puzzle.plot() # not tested |
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no need for the # in front
src/sage/combinat/skew_tableau.py
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| D[(a,b)]['north_west'] = '1' | ||
| D[(a,b)]['south_east'] = '1' | ||
| D[(a,b)]['south_west'] = '0' | ||
| (a, b) = (i, j) |
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remove all parentheses in this line and similar ones
src/sage/combinat/skew_tableau.py
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| dirs = ('north_east', 'north_west', 'south') | ||
| triangles = sorted(all_pieces.delta_pieces(), key=lambda p : ''.join(p[dir] for dir in dirs)) | ||
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| for (i,j) in D.keys(): |
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| for (i,j) in D.keys(): | |
| for i, j in D: |
src/sage/combinat/skew_tableau.py
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| dirs = ('north_east', 'north_west', 'south_east', 'south_west') | ||
| # Check what pieces have the desired boundaries | ||
| for piece in pieces: | ||
| if all(piece[dir] == D[(i,j)][dir] for dir in dirs if dir in D[(i,j)].keys()): |
3 participants
The bijection from Knutson-Tao puzzles to Littlewood-Richardson tableaux was implemented in the initial version of
sage.combinat.knutson_tao_puzzlesbut it was removed during revision. See #14141 (comment) and #14141 (comment)This is a new independent implementation.
Changes to
sage.combinat.knutso_tao_puzzles:PuzzleFilling.to_littlewood_richardson_tableauthat takes a puzzle filling and returns its corresponding Littlewood-Richardson tableau.PuzzleFilling._ne_to_south_paththat does one step of the above bijection.Changes to
sage.combinat.skew_tableau:SkewTableau.is_littlewood_richardsonthat checks if a tableau is Littlewood-RichardsonSkewTableau.to_knutson_tao_puzzlethat sends a Littlewood-Richardson tableau to a Knutson-Tao puzzle. This is the inverse ofPuzzleFilling.to_littlewood_richardson_tableau.Changes to
sage.combinat.partition:Partition.to_abacusthat converts a partition to a string of 0s and 1s representing its abacus.abacus_to_partitionwhich is the inverse of the above.📝 Checklist
⌛ Dependencies