Ribbon Shaped Tableaux¶
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sage.combinat.ribbon_shaped_tableau.
RibbonShapedTableau
¶ A ribbon shaped tableau.
For the purposes of this class, a ribbon shaped tableau is a skew tableau whose shape is a skew partition which:
- has at least one cell in row \(1\);
- has at least one cell in column \(1\);
- has exactly one cell in each of \(q\) consecutive diagonals, for some nonnegative integer \(q\).
A ribbon is given by a list of the rows from top to bottom.
EXAMPLES:
sage: x = RibbonShapedTableau([[None, None, None, 2, 3], [None, 1, 4, 5], [3, 2]]); x [[None, None, None, 2, 3], [None, 1, 4, 5], [3, 2]] sage: x.pp() . . . 2 3 . 1 4 5 3 2 sage: x.shape() [5, 4, 2] / [3, 1]
The entries labeled by
None
correspond to the inner partition. UsingNone
is optional; the entries will be shifted accordingly.sage: x = RibbonShapedTableau([[2,3],[1,4,5],[3,2]]); x.pp() . . . 2 3 . 1 4 5 3 2
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sage.combinat.ribbon_shaped_tableau.
RibbonShapedTableaux
¶ The set of all ribbon shaped tableaux.
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sage.combinat.ribbon_shaped_tableau.
Ribbon_class
¶ This exists solely for unpickling
Ribbon_class
objects.
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sage.combinat.ribbon_shaped_tableau.
StandardRibbonShapedTableaux
¶ The set of all standard ribbon shaped tableaux.
INPUT:
shape
– (optional) the composition shape of the rows
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sage.combinat.ribbon_shaped_tableau.
StandardRibbonShapedTableaux_shape
¶ Class of standard ribbon shaped tableaux of ribbon shape
shape
.EXAMPLES:
sage: StandardRibbonShapedTableaux([2,2]) Standard ribbon shaped tableaux of shape [2, 2] sage: StandardRibbonShapedTableaux([2,2]).first() [[None, 2, 4], [1, 3]] sage: StandardRibbonShapedTableaux([2,2]).last() [[None, 1, 2], [3, 4]] sage: StandardRibbonShapedTableaux([2,2]).cardinality() 5 sage: StandardRibbonShapedTableaux([2,2]).list() [[[None, 1, 3], [2, 4]], [[None, 1, 2], [3, 4]], [[None, 2, 3], [1, 4]], [[None, 2, 4], [1, 3]], [[None, 1, 4], [2, 3]]] sage: StandardRibbonShapedTableaux([3,2,2]).cardinality() 155