Optimization of add_*_border_strip() and doctest update.

src/sage/combinat/partition.py

@@ -318,8 +318,8 @@
 from . import permutation
 from . import composition
 from sage.combinat.partitions import ZS1_iterator, ZS1_iterator_nk
-from sage.combinat.integer_vector import IntegerVectors
 from sage.combinat.integer_lists import IntegerListsLex
+from sage.combinat.integer_lists.invlex import IntegerListsBackend_invlex
 from sage.combinat.integer_vector_weighted import iterator_fast as weighted_iterator_fast
 from sage.combinat.combinat_cython import conjugate
 from sage.combinat.root_system.weyl_group import WeylGroup
@@ -4655,67 +4655,101 @@ def add_vertical_border_strip(self, k):
 
  sage: Partition([]).add_vertical_border_strip(0)
  [[]]
+ sage: Partition([3,2,1]).add_vertical_border_strip(0)
+ [[3, 2, 1]]
  sage: Partition([]).add_vertical_border_strip(2)
  [[1, 1]]
  sage: Partition([2,2]).add_vertical_border_strip(2)
  [[3, 3], [3, 2, 1], [2, 2, 1, 1]]
  sage: Partition([3,2,2]).add_vertical_border_strip(2)
  [[4, 3, 2], [4, 2, 2, 1], [3, 3, 3], [3, 3, 2, 1], [3, 2, 2, 1, 1]]
  """
- return [p.conjugate() for p in self.conjugate().add_horizontal_border_strip(k)]
+ if k == 0:
+ return [self]
 
- def add_horizontal_border_strip(self, k):
- """
- Return a list of all the partitions that can be obtained by adding
- a horizontal border strip of length ``k`` to ``self``.
-
- EXAMPLES::
-
- sage: Partition([]).add_horizontal_border_strip(0)
- [[]]
- sage: Partition([]).add_horizontal_border_strip(2)
- [[2]]
- sage: Partition([2,2]).add_horizontal_border_strip(2)
- [[2, 2, 2], [3, 2, 1], [4, 2]]
- sage: Partition([3,2,2]).add_horizontal_border_strip(2)
- [[3, 2, 2, 2], [3, 3, 2, 1], [4, 2, 2, 1], [4, 3, 2], [5, 2, 2]]
-
- .. TODO::
-
- Reimplement like ``remove_horizontal_border_strip`` using
- :class:`IntegerListsLex`
- """
- conj = self.conjugate().to_list()
  shelf = []
  res = []
  i = 0
- while i < len(conj):
+ ell = len(self._list)
+ while i < ell:
  tmp = 1
- while i+1 < len(conj) and conj[i] == conj[i+1]:
+ while i+1 < ell and self._list[i] == self._list[i+1]:
  tmp += 1
  i += 1
- if i == len(conj)-1 and i > 0 and conj[i] != conj[i-1]:
+ if i == ell-1 and i > 0 and self._list[i] != self._list[i-1]:
  tmp = 1
  shelf.append(tmp)
  i += 1
 
- #added the last shelf on the right side of
- #the first line
+ # added the last shelf on the right side of
+ # the first line
  shelf.append(k)
 
- #list all of the positions for cells
- #filling each self from the left to the right
- for iv in IntegerVectors(k, len(shelf), outer=shelf):
- iv = list(iv) # Make a mutable list
- tmp = conj + [0]*k
+ # list all of the positions for cells
+ # filling each self from the left to the right
+ for iv in IntegerListsBackend_invlex(k, length=len(shelf), ceiling=shelf, check=False)._iter():
+ tmp = self._list + [0]*k
  j = 0
  for t in range(len(iv)):
- while iv[t] > 0:
+ for _ in range(iv[t]):
  tmp[j] += 1
- iv[t] -= 1
  j += 1
  j = sum(shelf[:t+1])
- res.append(Partition([u for u in tmp if u != 0]).conjugate())
+ # This should never return the empty partition.
+ # So tmp should never be [0, ..., 0].
+ while not tmp[-1]:
+ tmp.pop()
+ res.append(_Partitions(tmp))
+ return res
+
+ def add_horizontal_border_strip(self, k):
+ """
+ Return a list of all the partitions that can be obtained by adding
+ a horizontal border strip of length ``k`` to ``self``.
+
+ EXAMPLES::
+
+ sage: Partition([]).add_horizontal_border_strip(0)
+ [[]]
+ sage: Partition([3,2,1]).add_horizontal_border_strip(0)
+ [[3, 2, 1]]
+ sage: Partition([]).add_horizontal_border_strip(2)
+ [[2]]
+ sage: Partition([2,2]).add_horizontal_border_strip(2)
+ [[4, 2], [3, 2, 1], [2, 2, 2]]
+ sage: Partition([3,2,2]).add_horizontal_border_strip(2)
+ [[5, 2, 2], [4, 3, 2], [4, 2, 2, 1], [3, 3, 2, 1], [3, 2, 2, 2]]
+ """
+ if k == 0:
+ return [self]
+
+ L = self._list
+ res = []
+ mapping = [0]
+ shelf = [k]
+ for i in range(len(L)-1):
+ val = L[i] - L[i+1]
+ if not val:
+ continue
+ mapping.append(i+1)
+ shelf.append(val)
+
+ # add the last shelf
+ if L:
+ mapping.append(len(L))
+ shelf.append(L[-1])
+
+ # list all of the positions for cells
+ # filling each self from the top to bottom
+ for iv in IntegerListsBackend_invlex(k, length=len(shelf), ceiling=shelf, check=False)._iter():
+ tmp = self._list + [0]
+ for i, val in enumerate(iv):
+ if val:
+ tmp[mapping[i]] += val
+ # Only the last row is possibly empty
+ if not tmp[-1]:
+ tmp.pop()
+ res.append(_Partitions(tmp))
  return res
 
  def remove_horizontal_border_strip(self, k):
@@ -4839,7 +4873,7 @@ def atom(self):
  return res
 
  def k_atom(self, k):
- """
+ r"""
  Return a list of the standard tableaux of size ``self.size()`` whose
  ``k``-atom is equal to ``self``.
 
@@ -4849,12 +4883,12 @@ def k_atom(self, k):
  sage: p.k_atom(1)
  []
  sage: p.k_atom(3)
- [[[1, 1, 1], [2, 2], [3]],
- [[1, 1, 1, 2], [2], [3]],
+ [[[1, 1, 1, 2, 3], [2]],
  [[1, 1, 1, 3], [2, 2]],
- [[1, 1, 1, 2, 3], [2]]]
+ [[1, 1, 1, 2], [2], [3]],
+ [[1, 1, 1], [2, 2], [3]]]
  sage: Partition([3,2,1]).k_atom(4)
- [[[1, 1, 1], [2, 2], [3]], [[1, 1, 1, 3], [2, 2]]]
+ [[[1, 1, 1, 3], [2, 2]], [[1, 1, 1], [2, 2], [3]]]
 
  TESTS::
 

src/sage/combinat/superpartition.py

@@ -678,19 +678,19 @@ def add_horizontal_border_strip_star(self, h) -> list:
  EXAMPLES::
 
  sage: SuperPartition([[4,1],[3]]).add_horizontal_border_strip_star(3)
- [[4, 1; 3, 3],
- [4, 1; 4, 2],
- [3, 1; 5, 2],
- [4, 1; 5, 1],
+ [[3, 1; 7],
+ [4, 1; 6],
+ [3, 0; 6, 2],
  [3, 1; 6, 1],
- [4, 0; 4, 3],
- [3, 0; 5, 3],
  [4, 0; 5, 2],
- [3, 0; 6, 2],
- [4, 1; 6],
- [3, 1; 7]]
+ [4, 1; 5, 1],
+ [3, 0; 5, 3],
+ [3, 1; 5, 2],
+ [4, 0; 4, 3],
+ [4, 1; 4, 2],
+ [4, 1; 3, 3]]
  sage: SuperPartition([[2,1],[3]]).add_horizontal_border_strip_star(2)
- [[2, 1; 3, 2], [2, 1; 4, 1], [2, 0; 3, 3], [2, 0; 4, 2], [2, 1; 5]]
+ [[2, 1; 5], [2, 0; 4, 2], [2, 1; 4, 1], [2, 0; 3, 3], [2, 1; 3, 2]]
  """
  sp1, circ_list = self.to_circled_diagram()
  nsp = [list(la) + [0] for la in sp1.add_horizontal_border_strip(h)]
@@ -726,29 +726,29 @@ def add_horizontal_border_strip_star_bar(self, h) -> list:
  EXAMPLES::
 
  sage: SuperPartition([[4,1],[5,4]]).add_horizontal_border_strip_star_bar(3)
- [[4, 3; 5, 4, 1],
- [4, 1; 5, 4, 3],
- [4, 2; 5, 5, 1],
- [4, 1; 5, 5, 2],
+ [[4, 1; 8, 4],
+ [4, 1; 7, 5],
+ [4, 2; 7, 4],
+ [4, 1; 7, 4, 1],
+ [4, 2; 6, 5],
+ [4, 1; 6, 5, 1],
+ [4, 3; 6, 4],
  [4, 2; 6, 4, 1],
  [4, 1; 6, 4, 2],
- [4, 1; 6, 5, 1],
- [4, 1; 7, 4, 1],
  [4, 3; 5, 5],
- [4, 3; 6, 4],
- [4, 2; 6, 5],
- [4, 2; 7, 4],
- [4, 1; 7, 5],
- [4, 1; 8, 4]]
+ [4, 2; 5, 5, 1],
+ [4, 1; 5, 5, 2],
+ [4, 3; 5, 4, 1],
+ [4, 1; 5, 4, 3]]
  sage: SuperPartition([[3,1],[5]]).add_horizontal_border_strip_star_bar(2)
- [[3, 2; 5, 1],
- [3, 1; 5, 2],
- [4, 1; 5, 1],
+ [[3, 1; 7],
+ [4, 1; 6],
+ [3, 2; 6],
  [3, 1; 6, 1],
  [4, 2; 5],
- [3, 2; 6],
- [4, 1; 6],
- [3, 1; 7]]
+ [4, 1; 5, 1],
+ [3, 2; 5, 1],
+ [3, 1; 5, 2]]
  """
  sp1, circ_list = self.to_circled_diagram()
  nsp = [list(la) + [0] for la in sp1.add_horizontal_border_strip(h)]

src/sage/combinat/tableau.py

@@ -3239,26 +3239,26 @@ def promotion_operator(self, i):
 
  sage: t = Tableau([[1,2],[3]])
  sage: t.promotion_operator(1)
- [[[1, 2], [3], [4]], [[1, 2], [3, 4]], [[1, 2, 4], [3]]]
+ [[[1, 2, 4], [3]], [[1, 2], [3, 4]], [[1, 2], [3], [4]]]
  sage: t.promotion_operator(2)
- [[[1, 1], [2, 3], [4]],
- [[1, 1, 2], [3], [4]],
+ [[[1, 1, 2, 4], [3]],
  [[1, 1, 4], [2, 3]],
- [[1, 1, 2, 4], [3]]]
+ [[1, 1, 2], [3], [4]],
+ [[1, 1], [2, 3], [4]]]
  sage: Tableau([[1]]).promotion_operator(2)
- [[[1, 1], [2]], [[1, 1, 2]]]
+ [[[1, 1, 2]], [[1, 1], [2]]]
  sage: Tableau([[1,1],[2]]).promotion_operator(3)
- [[[1, 1, 1], [2, 2], [3]],
- [[1, 1, 1, 2], [2], [3]],
+ [[[1, 1, 1, 2, 3], [2]],
  [[1, 1, 1, 3], [2, 2]],
- [[1, 1, 1, 2, 3], [2]]]
+ [[1, 1, 1, 2], [2], [3]],
+ [[1, 1, 1], [2, 2], [3]]]
 
  The example from [LLM2003]_ p. 12::
 
  sage: Tableau([[1,1],[2,2]]).promotion_operator(3)
- [[[1, 1, 1], [2, 2], [3, 3]],
+ [[[1, 1, 1, 3, 3], [2, 2]],
  [[1, 1, 1, 3], [2, 2], [3]],
- [[1, 1, 1, 3, 3], [2, 2]]]
+ [[1, 1, 1], [2, 2], [3, 3]]]
 
  TESTS::