Add examples and fix bug

src/sage/combinat/permutation.py

@@ -2994,6 +2994,15 @@ def reduced_word_lexmin(self):
     def rothe_diagram(self):
         r"""
         Return the Rothe diagram of ``self``.
+
+        EXAMPLES::
+
+            sage: w = Permutation([1,4,3,2])
+            sage: w.rothe_diagram().pp()
+            . . . .
+            . O O .
+            . O . .
+            . . . .
         """
         from sage.combinat.diagram import RotheDiagram
         return RotheDiagram(self)
@@ -3002,9 +3011,14 @@ def n_reduced_words(self):
         r"""
         Return the number of reduced words of ``self`` without explicitly
         computing them all.
+
+        EXAMPLES::
+
+            sage: w = Permutation([1,4,3,2])
+            sage: w.n_reduced_words()
+            2
         """
         Tx = self.rothe_diagram().peelable_tableaux()
-
         return sum(map(_tableau_contribution, Tx))
 
     def stanley_symmetric_function(self):
@@ -5282,7 +5296,10 @@ def _tableau_contribution(T):
     r"""
     Get the number of SYT of shape(``T``).
     """
+    from sage.combinat.tableau import StandardTableaux
     return(StandardTableaux(T.shape()).cardinality())
+
+
 ################################################################
 # Parent classes
 ################################################################