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Package sage :: Package combinat :: Package sf :: Module ns_macdonald :: Class LatticeDiagram
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Class LatticeDiagram

source code

                      object --+        
                               |        
structure.sage_object.SageObject --+    
                                   |    
        combinat.CombinatorialObject --+
                                       |
                                      LatticeDiagram
Instance Methods [hide private]
 
boxes(self)
EXAMPLES:...		 source code
 
__getitem__(self, i)
Returns the $i^{th}$ entry of self.		 source code
 
leg(self, i, j)
Returns the leg of the box (i,j) in self.		 source code
 
arm_left(self, i, j)
Returns the left arm of the box (i,j) in self.		 source code
 
arm_right(self, i, j)
Returns the right arm of the box (i,j) in self.		 source code
 
arm(self, i, j)
Returns the arm of the box (i,j) in self.		 source code
 
l(self, i, j)
Returns the self[i] - j.		 source code
 
a(self, i, j)
Returns len(self.arm(i,j)).		 source code
 
size(self)
Returns the number of boxes in self.		 source code
 
flip(self)
Returns the flip of the self where flip is defined as follows.		 source code
 
boxes_same_and_lower_right(self, ii, jj)
Returns a list of the boxes that are in the same row as self, and in the row below self (including the basement) that are strictly to the right of self.		 source code

Inherited from combinat.CombinatorialObject: __add__, __contains__, __eq__, __ge__, __gt__, __hash__, __init__, __iter__, __le__, __len__, __lt__, __ne__, __repr__, __str__, index

Inherited from structure.sage_object.SageObject: __new__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, category, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce__, __reduce_ex__, __setattr__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

boxes(self)

source code  

EXAMPLES:
    sage: a = LatticeDiagram([3,0,2])
    sage: a.boxes()
    [(1, 1), (1, 2), (1, 3), (3, 1), (3, 2)]
    sage: a = LatticeDiagram([2, 1, 3, 0, 0, 2])
    sage: a.boxes()
    [(1, 1), (1, 2), (2, 1), (3, 1), (3, 2), (3, 3), (6, 1), (6, 2)]

__getitem__(self, i)
(Indexing operator)

source code  

Returns the $i^{th}$ entry of self. Note that the
indexing starts for lattice diagrams starts at 1.

EXAMPLES:
    sage: a = LatticeDiagram([3,0,2])
    sage: a[1]
    3
    sage: a[0]
    Traceback (most recent call last):
    ...
    ValueError: indexing starts at 1
    sage: a[-1]
    2
Overrides: combinat.CombinatorialObject.__getitem__

leg(self, i, j)

source code  

Returns the leg of the box (i,j) in self.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.leg(5,2)
    [(5, 3)]

arm_left(self, i, j)

source code  

Returns the left arm of the box (i,j) in self.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.arm_left(5,2)
    [(1, 2), (3, 2)]

arm_right(self, i, j)

source code  

Returns the right arm of the box (i,j) in self.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.arm_right(5,2)
    [(8, 1)]

arm(self, i, j)

source code  

Returns the arm of the box (i,j) in self.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.arm(5,2)
    [(1, 2), (3, 2), (8, 1)]

l(self, i, j)

source code  

Returns the self[i] - j.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.l(5,2)
    1

a(self, i, j)

source code  

Returns len(self.arm(i,j)).

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.a(5,2)
    3

size(self)

source code  

Returns the number of boxes in self.

EXAMPLES:
    sage: a = LatticeDiagram([3,1,2,4,3,0,4,2,3])
    sage: a.size()
    22

flip(self)

source code  

Returns the flip of the self where flip is defined as follows.
Let r = max(self).  Then self.flip()[i] = r - self[i].

EXAMPLES:
    sage: a = LatticeDiagram([3,0,2])
    sage: a.flip()
    [0, 3, 1]

boxes_same_and_lower_right(self, ii, jj)

source code  

Returns a list of the boxes that are in the same row as self, and in the
row below self (including the basement) that are strictly to the
right of self.

EXAMPLES:
    sage: a = AugmentedLatticeDiagramFilling([[1,6],[2],[3,4,2],[],[],[5,5]])
    sage: a = a.shape()
    sage: a.boxes_same_and_lower_right(1,1)
    [(2, 1), (3, 1), (6, 1), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0)]
    sage: a.boxes_same_and_lower_right(1,2)
    [(3, 2), (6, 2), (2, 1), (3, 1), (6, 1)]
    sage: a.boxes_same_and_lower_right(3,3)
    [(6, 2)]
    sage: a.boxes_same_and_lower_right(2,3)
    [(3, 3), (3, 2), (6, 2)]

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