Ticket #12569: trac_12569-permutohedron_intervals-sg.patch

sage/combinat/permutation.py

@@ -2422 +2422 @@
         return transitive_ideal(lambda x: x.permutohedron_succ(side), self)
 
 
+    def right_permutohedron_interval_iterator(self, other) :
+        r"""
+        Returns an iterator on the permutations (represented as integer
+        lists) belonging to the right permutohedron interval where `self`
+        is the minimal element and `other`, the maximal.
+        """
+        if len(self) != len(other) :
+            raise ValueError,\
+            "len(%s) and len(%s) must be equal" %(self, other)
+        if not self.permutohedron_lequal(other) :
+            raise ValueError,\
+            "%s must be lower or equal than %s for the right permutohedron order"\
+            %(self, other)
+        from sage.graphs.digraph import DiGraph
+        d = DiGraph()
+        d.add_vertices(xrange(1, len(self) + 1))
+        d.add_edges([(j + 1, i + 1) for (i, j) in self.inverse().inversions()])
+        d.add_edges([(other[i], other[j]) for i in xrange(len(other) - 1)\
+        for j in xrange(i, len(other)) if other[i] < other[j]])
+        from sage.graphs.linearextensions import LinearExtensions
+        return LinearExtensions(d)
+
+    def right_permutohedron_interval(self, other) :
+        r"""
+        Returns the list of the permutations belonging to the right
+        permutohedron interval where `self` is the minimal element and
+        `other`, the maximal.
+
+        EXAMPLES::
+
+            sage: Permutation([2, 1, 4, 5, 3]).right_permutohedron_interval(Permutation([2, 5, 4, 1, 3]))
+            [[2, 1, 4, 5, 3], [2, 1, 5, 4, 3], [2, 4, 1, 5, 3], [2, 4, 5, 1, 3], [2, 5, 1, 4, 3], [2, 5, 4, 1, 3]]
+
+        TESTS::
+
+            sage: Permutation([]).right_permutohedron_interval(Permutation([]))
+            [[]]
+            sage: Permutation([3, 1, 2]).right_permutohedron_interval(Permutation([3, 1, 2]))
+            [[3, 1, 2]]
+            sage: Permutation([1, 3, 2, 4]).right_permutohedron_interval(Permutation([3, 4, 2, 1]))
+            [[1, 3, 2, 4], [1, 3, 4, 2], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1]]
+            sage: Permutation([2, 1, 4, 5, 3]).right_permutohedron_interval(Permutation([2, 5, 4, 1, 3]))
+            [[2, 1, 4, 5, 3], [2, 1, 5, 4, 3], [2, 4, 1, 5, 3], [2, 4, 5, 1, 3], [2, 5, 1, 4, 3], [2, 5, 4, 1, 3]]
+        """
+        return [Permutation(p) for p in self.right_permutohedron_interval_iterator(other)]
+
     ############
     # Patterns #
     ############