diff --git a/Eigen/src/Core/PermutationMatrix.h b/Eigen/src/Core/PermutationMatrix.h
index 8c9afd4ee..e8236cbd7 100644
--- a/Eigen/src/Core/PermutationMatrix.h
+++ b/Eigen/src/Core/PermutationMatrix.h
@@ -397,12 +397,12 @@ class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompile
 #ifndef EIGEN_PARSED_BY_DOXYGEN
     template<typename Other>
     PermutationMatrix(const Transpose<PermutationBase<Other> >& other)
-      : m_indices(other.nestedPermutation().size())
+      : m_indices(other.nestedExpression().size())
     {
       eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
       StorageIndex end = StorageIndex(m_indices.size());
       for (StorageIndex i=0; i<end;++i)
-        m_indices.coeffRef(other.nestedPermutation().indices().coeff(i)) = i;
+        m_indices.coeffRef(other.nestedExpression().indices().coeff(i)) = i;
     }
     template<typename Lhs,typename Rhs>
     PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
@@ -635,7 +635,7 @@ class Transpose<PermutationBase<Derived> >
       return Product<Transpose, OtherDerived, DefaultProduct>(*this, matrix.derived());
     }
 
-    const PermutationType& nestedPermutation() const { return m_permutation; }
+    const PermutationType& nestedExpression() const { return m_permutation; }
 
   protected:
     const PermutationType& m_permutation;
diff --git a/Eigen/src/Core/Product.h b/Eigen/src/Core/Product.h
index 7f0a9b589..0739528f1 100644
--- a/Eigen/src/Core/Product.h
+++ b/Eigen/src/Core/Product.h
@@ -53,6 +53,18 @@ template<typename Lhs, typename Rhs, typename LhsShape>
   typedef typename Lhs::Scalar Scalar;
 };
 
+template<typename Lhs, typename Rhs, typename RhsShape>
+struct product_result_scalar<Lhs, Rhs, TranspositionsShape, RhsShape>
+{
+  typedef typename Rhs::Scalar Scalar;
+};
+
+template<typename Lhs, typename Rhs, typename LhsShape>
+  struct product_result_scalar<Lhs, Rhs, LhsShape, TranspositionsShape>
+{
+  typedef typename Lhs::Scalar Scalar;
+};
+
 template<typename Lhs, typename Rhs, int Option>
 struct traits<Product<Lhs, Rhs, Option> >
 {
diff --git a/Eigen/src/Core/ProductEvaluators.h b/Eigen/src/Core/ProductEvaluators.h
index 4c673a6cb..5765857ce 100644
--- a/Eigen/src/Core/ProductEvaluators.h
+++ b/Eigen/src/Core/ProductEvaluators.h
@@ -915,7 +915,7 @@ struct generic_product_impl<Transpose<Lhs>, Rhs, PermutationShape, MatrixShape,
   template<typename Dest>
   static void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
   {
-    permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedPermutation(), rhs);
+    permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
   }
 };
 
@@ -925,7 +925,7 @@ struct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, PermutationShape,
   template<typename Dest>
   static void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
   {
-    permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedPermutation(), lhs);
+    permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
   }
 };
 
@@ -944,7 +944,7 @@ template<typename MatrixType, int Side, bool Transposed, typename MatrixShape>
 struct transposition_matrix_product
 {
     template<typename Dest, typename TranspositionType>
-    static inline void evalTo(Dest& dst, const TranspositionType& tr, const MatrixType& mat)
+    static inline void run(Dest& dst, const TranspositionType& tr, const MatrixType& mat)
     {
       typedef typename TranspositionType::StorageIndex StorageIndex;
       const Index size = tr.size();
@@ -982,13 +982,14 @@ struct generic_product_impl<Lhs, Rhs, MatrixShape, TranspositionsShape, ProductT
   }
 };
 
+
 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
 struct generic_product_impl<Transpose<Lhs>, Rhs, TranspositionsShape, MatrixShape, ProductTag>
 {
   template<typename Dest>
   static void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
   {
-    transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedPermutation(), rhs);
+    transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
   }
 };
 
@@ -998,7 +999,7 @@ struct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, TranspositionsShap
   template<typename Dest>
   static void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
   {
-    transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedPermutation(), lhs);
+    transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
   }
 };
 
diff --git a/Eigen/src/Core/Transpositions.h b/Eigen/src/Core/Transpositions.h
index dad4f56c9..65447745f 100644
--- a/Eigen/src/Core/Transpositions.h
+++ b/Eigen/src/Core/Transpositions.h
@@ -62,7 +62,7 @@ class TranspositionsBase
       indices() = other.indices();
       return derived();
     }
-
+    
     #ifndef EIGEN_PARSED_BY_DOXYGEN
     /** This is a special case of the templated operator=. Its purpose is to
       * prevent a default operator= from hiding the templated operator=.
@@ -75,7 +75,11 @@ class TranspositionsBase
     #endif
 
     /** \returns the number of transpositions */
-    inline Index size() const { return indices().size(); }
+    Index size() const { return indices().size(); }
+    /** \returns the number of rows of the equivalent permutation matrix */
+    Index rows() const { return indices().size(); }
+    /** \returns the number of columns of the equivalent permutation matrix */
+    Index cols() const { return indices().size(); }
 
     /** Direct access to the underlying index vector */
     inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
@@ -143,9 +147,10 @@ class TranspositionsBase
 namespace internal {
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
+ : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
   typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
-  typedef _StorageIndex StorageIndex;
+  typedef TranspositionsStorage StorageKind;
 };
 }
 
@@ -214,9 +219,11 @@ class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTim
 namespace internal {
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>
 struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,_PacketAccess> >
+ : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
   typedef Map<const Matrix<_StorageIndex,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
   typedef _StorageIndex StorageIndex;
+  typedef TranspositionsStorage StorageKind;
 };
 }
 
@@ -271,9 +278,9 @@ class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,P
 namespace internal {
 template<typename _IndicesType>
 struct traits<TranspositionsWrapper<_IndicesType> >
+ : traits<PermutationWrapper<_IndicesType> >
 {
-  typedef typename _IndicesType::Scalar StorageIndex;
-  typedef _IndicesType IndicesType;
+  typedef TranspositionsStorage StorageKind;
 };
 }
 
@@ -347,8 +354,16 @@ operator*(const TranspositionsBase<TranspositionsDerived> &transpositions,
             (transpositions.derived(), matrix.derived());
 }
 
+// Template partial specialization for transposed/inverse transpositions
 
-/* Template partial specialization for transposed/inverse transpositions */
+namespace internal {
+
+template<typename Derived>
+struct traits<Transpose<TranspositionsBase<Derived> > >
+ : traits<Derived>
+{};
+
+} // end namespace internal
 
 template<typename TranspositionsDerived>
 class Transpose<TranspositionsBase<TranspositionsDerived> >
@@ -359,7 +374,9 @@ class Transpose<TranspositionsBase<TranspositionsDerived> >
 
     explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}
 
-    inline int size() const { return m_transpositions.size(); }
+    Index size() const { return m_transpositions.size(); }
+    Index rows() const { return m_transpositions.size(); }
+    Index cols() const { return m_transpositions.size(); }
 
     /** \returns the \a matrix with the inverse transpositions applied to the columns.
       */
@@ -378,6 +395,8 @@ class Transpose<TranspositionsBase<TranspositionsDerived> >
     {
       return Product<Transpose, OtherDerived, DefaultProduct>(*this, matrix.derived());
     }
+    
+    const TranspositionType& nestedExpression() const { return m_transpositions; }
 
   protected:
     const TranspositionType& m_transpositions;
diff --git a/Eigen/src/Core/util/Constants.h b/Eigen/src/Core/util/Constants.h
index 3e6c75444..8d6089b2d 100644
--- a/Eigen/src/Core/util/Constants.h
+++ b/Eigen/src/Core/util/Constants.h
@@ -468,6 +468,9 @@ struct Sparse {};
 /** The type used to identify a permutation storage. */
 struct PermutationStorage {};
 
+/** The type used to identify a permutation storage. */
+struct TranspositionsStorage {};
+
 /** The type used to identify a matrix expression */
 struct MatrixXpr {};