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diff --git a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Ordered_set_partition_iterator.h b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Ordered_set_partition_iterator.h
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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef PERMUTAHEDRAL_REPRESENTATION_ORDERED_SET_PARTITION_ITERATOR_H_
+#define PERMUTAHEDRAL_REPRESENTATION_ORDERED_SET_PARTITION_ITERATOR_H_
+
+#include <vector>
+#include <limits>
+
+#include <gudhi/Permutahedral_representation/Permutation_iterator.h>
+#include <gudhi/Permutahedral_representation/Set_partition_iterator.h>
+
+#include <boost/range/iterator_range.hpp>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+typedef unsigned uint;
+
+/** \brief Class that represents an ordered set partition of a set {0,...,n-1} in k parts as
+ *         a pair of an unordered set partition given in lexicographic order and
+ *         a permutation of the parts.
+ */
+struct Ordered_set_partition {
+  Set_partition_iterator s_it_;
+  Permutation_iterator p_it_;
+
+  // Ordered_set_partition(const Set_partition_iterator& s_it, const Permutation_iterator& p_it)
+  //   : s_it_(s_it), p_it_(p_it) {}
+
+  const std::vector<uint> operator[](const uint& i) const { return (*s_it_)[(*p_it_)[i]]; }
+
+  std::size_t size() const { return s_it_->size(); }
+};
+
+/** \brief Class that allows the user to generate set partitions of a set {0,...,n-1} in k parts.
+ *
+ */
+class Ordered_set_partition_iterator
+    : public boost::iterator_facade<Ordered_set_partition_iterator, Ordered_set_partition const,
+                                    boost::forward_traversal_tag> {
+  using value_t = Ordered_set_partition;
+
+ private:
+  friend class boost::iterator_core_access;
+
+  bool equal(Ordered_set_partition_iterator const& other) const { return (is_end_ && other.is_end_); }
+
+  value_t const& dereference() const { return value_; }
+
+  void increment() {
+    if (++value_.p_it_ == p_end_) {
+      if (++value_.s_it_ == s_end_) {
+        is_end_ = true;
+        return;
+      } else
+        value_.p_it_.reinitialize();
+    }
+  }
+
+ public:
+  Ordered_set_partition_iterator(const uint& n, const uint& k)
+      : value_({Set_partition_iterator(n, k), Permutation_iterator(k)}), is_end_(n == 0) {}
+
+  // Used for the creating an end iterator
+  Ordered_set_partition_iterator() : is_end_(true) {}
+
+  void reinitialize() {
+    is_end_ = false;
+    value_.p_it_.reinitialize();
+    value_.s_it_.reinitialize();
+  }
+
+ private:
+  Set_partition_iterator s_end_;  // Set partition iterator and the corresponding end iterator
+  Permutation_iterator p_end_;    // Permutation iterator and the corresponding end iterator
+  value_t value_;                 // the dereference value
+  bool is_end_;                   // is true when the current permutation is the final one
+};
+
+}  // namespace coxeter_triangulation
+
+}  // namespace Gudhi
+
+#endif