Trac #34339: Speedup adding horizontal and vertical border strips

We can be better about the number of conjugations involved.

URL: https://trac.sagemath.org/34339
Reported by: tscrim
Ticket author(s): Travis Scrimshaw
Reviewer(s): Frédéric Chapoton

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::
 

src/sage/tests/book_schilling_zabrocki_kschur_primer.py

@@ -542,7 +542,7 @@
 
     sage: la = Partition([3,2,1,1])
     sage: la.k_atom(4)
-    [[[1, 1, 1], [2, 2], [3], [4]], [[1, 1, 1, 4], [2, 2], [3]]]
+    [[[1, 1, 1, 4], [2, 2], [3]], [[1, 1, 1], [2, 2], [3], [4]]]
 
 Sage example in ./kschurnotes/notes-mike-anne.tex, line 3639::