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diff --git a/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Combination_iterator.h b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Combination_iterator.h
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+++ b/src/Coxeter_triangulation/include/gudhi/Permutahedral_representation/Combination_iterator.h
@@ -0,0 +1,83 @@
+/*    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_COMBINATION_ITERATOR_H_
+#define PERMUTAHEDRAL_REPRESENTATION_COMBINATION_ITERATOR_H_
+
+#include <vector>
+#include <boost/range/iterator_range.hpp>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+typedef unsigned uint;
+
+/** \brief Class that allows the user to generate combinations of
+ *   k elements in a set of n elements.
+ *  Based on the algorithm by Mifsud.
+ */
+class Combination_iterator
+    : public boost::iterator_facade<Combination_iterator, std::vector<uint> const, boost::forward_traversal_tag> {
+  typedef std::vector<uint> value_t;
+
+ protected:
+  friend class boost::iterator_core_access;
+
+  bool equal(Combination_iterator const& other) const { return (is_end_ && other.is_end_); }
+
+  value_t const& dereference() const { return value_; }
+
+  void increment() {
+    if (value_[0] == n_ - k_) {
+      is_end_ = true;
+      return;
+    }
+    uint j = k_ - 1;
+    if (value_[j] < n_ - 1) {
+      value_[j]++;
+      return;
+    }
+    for (; j > 0; --j)
+      if (value_[j - 1] < n_ - k_ + j - 1) {
+        value_[j - 1]++;
+        for (uint s = j; s < k_; s++) value_[s] = value_[j - 1] + s - (j - 1);
+        return;
+      }
+  }
+
+ public:
+  Combination_iterator(const uint& n, const uint& k) : value_(k), is_end_(n == 0), n_(n), k_(k) {
+    for (uint i = 0; i < k; ++i) value_[i] = i;
+  }
+
+  // Used for the creating an end iterator
+  Combination_iterator() : is_end_(true), n_(0), k_(0) {}
+
+  void reinitialize() {
+    if (n_ > 0) {
+      is_end_ = false;
+      for (uint i = 0; i < n_; ++i) value_[i] = i;
+    }
+  }
+
+ private:
+  value_t value_;  // the dereference value
+  bool is_end_;    // is true when the current permutation is the final one
+
+  uint n_;
+  uint k_;
+};
+
+}  // namespace coxeter_triangulation
+
+}  // namespace Gudhi
+
+#endif