diff --git a/src/sage/categories/crystals.py b/src/sage/categories/crystals.py
index f19a7d963ee..cc2b5042969 100644
--- a/src/sage/categories/crystals.py
+++ b/src/sage/categories/crystals.py
@@ -16,12 +16,11 @@
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
 from __future__ import print_function
 from builtins import zip
-from six import itervalues
 
 from sage.misc.cachefunc import cached_method
 from sage.misc.abstract_method import abstract_method
@@ -789,7 +788,7 @@ def crystal_morphism(self, on_gens, codomain=None,
                         codomain = on_gens[0].parent()
                 elif isinstance(on_gens, dict):
                     if on_gens:
-                        codomain = next(itervalues(on_gens)).parent()
+                        codomain = next(iter(on_gens.values())).parent()
                 else:
                     for x in self.module_generators:
                         y = on_gens(x)
diff --git a/src/sage/combinat/alternating_sign_matrix.py b/src/sage/combinat/alternating_sign_matrix.py
index 9ff0b58199e..1489cc7221c 100644
--- a/src/sage/combinat/alternating_sign_matrix.py
+++ b/src/sage/combinat/alternating_sign_matrix.py
@@ -32,7 +32,7 @@
 # ****************************************************************************
 from __future__ import division
 from six.moves import range, zip
-from six import itervalues, add_metaclass
+from six import add_metaclass
 
 import copy
 from sage.misc.classcall_metaclass import ClasscallMetaclass
@@ -1495,7 +1495,7 @@ def _lattice_initializer(self):
         """
         mts, rels = MonotoneTriangles(self._n)._lattice_initializer()
         bij = {t: self.from_monotone_triangle(t) for t in mts}
-        return (itervalues(bij), [(bij[a], bij[b]) for (a, b) in rels])
+        return (bij.values(), [(bij[a], bij[b]) for (a, b) in rels])
 
     def cover_relations(self):
         r"""
diff --git a/src/sage/combinat/growth.py b/src/sage/combinat/growth.py
index 4feb5b52b3c..141fe345d4b 100644
--- a/src/sage/combinat/growth.py
+++ b/src/sage/combinat/growth.py
@@ -1402,8 +1402,7 @@ def _process_filling_and_shape(self, filling, shape):
         """
         if isinstance(filling, dict):
             try:
-                from six import itervalues
-                v = next(itervalues(filling))
+                v = next(iter(filling.values()))
                 if isinstance(v, dict):
                     # it is a dict of dicts
                     F = dict()
diff --git a/src/sage/combinat/permutation.py b/src/sage/combinat/permutation.py
index 64b08f01ba1..a68d6734f81 100644
--- a/src/sage/combinat/permutation.py
+++ b/src/sage/combinat/permutation.py
@@ -229,15 +229,13 @@
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 from __future__ import print_function, absolute_import
 
 from builtins import zip
 from six.moves import range
 
-from six import itervalues
-
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
@@ -248,7 +246,7 @@
 from sage.structure.global_options import GlobalOptions
 from sage.interfaces.all import gap
 from sage.rings.all import ZZ, Integer, PolynomialRing
-from sage.arith.all import factorial
+from sage.arith.all import factorial, multinomial
 from sage.matrix.matrix_space import MatrixSpace
 from sage.combinat.tools import transitive_ideal
 from sage.combinat.composition import Composition
@@ -5507,8 +5505,8 @@ def cardinality(self):
             sage: Permutations(3,4).cardinality()
             0
         """
-        if self._k <= self.n and self._k >= 0:
-            return factorial(self.n) // factorial(self.n-self._k)
+        if 0 <= self._k <= self.n:
+            return factorial(self.n) // factorial(self.n - self._k)
         return ZZ.zero()
 
     def random_element(self):
@@ -5684,11 +5682,8 @@ def cardinality(self):
         for i in mset_list:
             d[i] = d.get(i, 0) + 1
 
-        c = factorial(len(lmset))
-        for i in itervalues(d):
-            if i != 1:
-                c //= factorial(i)
-        return ZZ(c)
+        return ZZ(multinomial(d.values()))
+
 
 class Permutations_set(Permutations):
     """
diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index 65274d8bf4b..e9185d24973 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -90,7 +90,6 @@
 # ****************************************************************************
 from __future__ import print_function
 
-import six
 from six.moves import range
 import itertools
 
@@ -393,7 +392,7 @@ def __init__(self, data, domain=None, codomain=None):
             self._morph = {}
 
             dom_alph = list()
-            for (key,val) in six.iteritems(data):
+            for key, val in data.items():
                 dom_alph.append(key)
                 if val in codomain.alphabet():
                     self._morph[key] = codomain([val])
@@ -474,7 +473,7 @@ def _build_codomain(self, data):
             Finite words over {0, 1, 2}
         """
         codom_alphabet = set()
-        for key,val in six.iteritems(data):
+        for key, val in data.items():
             try:
                 it = iter(val)
             except Exception:
@@ -490,7 +489,7 @@ def __hash__(self):
             sage: hash(WordMorphism('a->ab,b->ba')) # random
             7211091143079804375
         """
-        return hash(tuple((k,v) for k,v in six.iteritems(self._morph))) ^ hash(self._codomain)
+        return hash(tuple((k,v) for k,v in self._morph.items())) ^ hash(self._codomain)
 
     def __eq__(self, other):
         r"""
@@ -603,7 +602,8 @@ def __str__(self):
             sage: str(s)
             'a->ab, b->ba'
         """
-        L = [str(lettre) + '->' + image.string_rep() for lettre,image in six.iteritems(self._morph)]
+        L = [str(lettre) + '->' + image.string_rep()
+             for lettre, image in self._morph.items()]
         return ', '.join(sorted(L))
 
     def __call__(self, w, order=1, datatype=None):
@@ -977,7 +977,7 @@ def __mul__(self, other):
             sage: m * WordMorphism('')
             WordMorphism:
         """
-        return WordMorphism(dict((key, self(w)) for (key, w) in six.iteritems(other._morph)), codomain=self.codomain())
+        return WordMorphism(dict((key, self(w)) for key, w in other._morph.items()), codomain=self.codomain())
 
     def __pow__(self, exp):
         r"""
@@ -1082,7 +1082,7 @@ def extend_by(self, other):
             raise TypeError("other (=%s) is not a WordMorphism"%other)
 
         nv = dict(other._morph)
-        for k,v in six.iteritems(self._morph):
+        for k, v in self._morph.items():
             nv[k] = v
         return WordMorphism(nv)
 
@@ -1290,7 +1290,7 @@ def images(self):
             sage: sorted(WordMorphism('6->ab,y->5,0->asd').images())
             [word: 5, word: ab, word: asd]
         """
-        return list(six.itervalues(self._morph))
+        return list(self._morph.values())
 
     def reversal(self):
         r"""
@@ -1303,7 +1303,7 @@ def reversal(self):
             sage: WordMorphism('a->ab,b->a').reversal()
             WordMorphism: a->ba, b->a
         """
-        return WordMorphism(dict((key, w.reversal()) for (key, w) in six.iteritems(self._morph)),codomain=self._codomain)
+        return WordMorphism(dict((key, w.reversal()) for (key, w) in self._morph.items()),codomain=self._codomain)
 
     def is_empty(self):
         r"""
@@ -2186,7 +2186,7 @@ def conjugate(self, pos):
             sage: m.conjugate(2)
             WordMorphism: a->cdeab, b->zxy
         """
-        return WordMorphism(dict((key, w.conjugate(pos)) for (key, w) in six.iteritems(self._morph)))
+        return WordMorphism(dict((key, w.conjugate(pos)) for (key, w) in self._morph.items()))
 
     def has_left_conjugate(self):
         r"""
diff --git a/src/sage/data_structures/mutable_poset.py b/src/sage/data_structures/mutable_poset.py
index 530b423bb53..6df1357c03c 100644
--- a/src/sage/data_structures/mutable_poset.py
+++ b/src/sage/data_structures/mutable_poset.py
@@ -150,8 +150,6 @@
 # ****************************************************************************
 from __future__ import print_function
 
-from six import itervalues
-
 from sage.structure.sage_object import SageObject
 
 
@@ -1690,7 +1688,7 @@ def _copy_shells_(self, other, mapping):
         self._null_ = other._null_._copy_all_linked_(memo, self, mapping)
         self._oo_ = memo[id(other._oo_)]
         self._shells_ = {f.key: f for f in iter(memo[id(e)] for e in
-                                                itervalues(other._shells_))}
+                                                other._shells_.values())}
 
     def copy(self, mapping=None):
         r"""
@@ -1771,7 +1769,7 @@ def shells(self, include_special=False):
         """
         if include_special:
             yield self.null
-        for e in itervalues(self._shells_):
+        for e in self._shells_.values():
             yield e
         if include_special:
             yield self.oo
diff --git a/src/sage/databases/conway.py b/src/sage/databases/conway.py
index b2a984628c3..a5a96f64059 100644
--- a/src/sage/databases/conway.py
+++ b/src/sage/databases/conway.py
@@ -19,7 +19,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from six import itervalues, iteritems
+from six import iteritems
 from six.moves import cPickle as pickle
 
 import collections
@@ -168,7 +168,7 @@ def __len__(self):
             return self._len
         except AttributeError:
             pass
-        self._len = sum(len(a) for a in itervalues(self._store))
+        self._len = sum(len(a) for a in self._store.values())
         return self._len
 
     def __iter__(self):
diff --git a/src/sage/graphs/graph.py b/src/sage/graphs/graph.py
index 6450e9574ef..2d8a0b7dd48 100644
--- a/src/sage/graphs/graph.py
+++ b/src/sage/graphs/graph.py
@@ -6975,7 +6975,7 @@ def cores(self, k=None, with_labels=False):
         if with_labels:
             return core
         else:
-            return list(six.itervalues(core))
+            return list(core.values())
 
     @doc_index("Leftovers")
     def modular_decomposition(self, algorithm='habib'):
diff --git a/src/sage/knots/link.py b/src/sage/knots/link.py
index 36ddf4df387..eda927fb177 100644
--- a/src/sage/knots/link.py
+++ b/src/sage/knots/link.py
@@ -48,7 +48,6 @@
 # ****************************************************************************
 from __future__ import division
 
-import six
 from six.moves import range
 
 from sage.matrix.constructor import matrix
@@ -1340,7 +1339,7 @@ def pd_code(self):
             else:
                 crossing_dic = {}
 
-            pd = list(six.itervalues(crossing_dic))
+            pd = list(crossing_dic.values())
             self._pd_code = pd
             return self._pd_code
 
diff --git a/src/sage/matroids/constructor.py b/src/sage/matroids/constructor.py
index 07e365e0254..fede3652de5 100644
--- a/src/sage/matroids/constructor.py
+++ b/src/sage/matroids/constructor.py
@@ -97,13 +97,11 @@
 #  Distributed under the terms of the GNU General Public License (GPL)
 #  as published by the Free Software Foundation; either version 2 of
 #  the License, or (at your option) any later version.
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
 from __future__ import absolute_import
 
-from six import itervalues
-
 from itertools import combinations
 from sage.matrix.constructor import Matrix
 from sage.graphs.all import Graph
@@ -917,7 +915,7 @@ def revlex_sort_key(s):
 
         if groundset is None:
             groundset = set()
-            for X in itervalues(CC):
+            for X in CC.values():
                 for Y in X:
                     groundset.update(Y)
 
diff --git a/src/sage/misc/sage_input.py b/src/sage/misc/sage_input.py
index b811e98652e..3b1b978d37b 100644
--- a/src/sage/misc/sage_input.py
+++ b/src/sage/misc/sage_input.py
@@ -174,7 +174,7 @@
 
 from __future__ import print_function, absolute_import
 
-from six import itervalues, iteritems, integer_types, string_types
+from six import iteritems, integer_types, string_types
 
 
 def sage_input(x, preparse=True, verify=False, allow_locals=False):
@@ -1915,7 +1915,7 @@ def _sie_referenced(self):
         """
         refs = self._sie_args[:]
         refs.append(self._sie_func)
-        refs.extend(itervalues(self._sie_kwargs))
+        refs.extend(self._sie_kwargs.values())
         return refs
 
     def _sie_format(self, sif):
diff --git a/src/sage/modular/pollack_stevens/manin_map.py b/src/sage/modular/pollack_stevens/manin_map.py
index 36ea54103c2..e5118e89d7a 100644
--- a/src/sage/modular/pollack_stevens/manin_map.py
+++ b/src/sage/modular/pollack_stevens/manin_map.py
@@ -43,7 +43,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 from __future__ import print_function, absolute_import
-from six import itervalues, iteritems
+from six import iteritems
 from six.moves import range
 
 from sage.rings.continued_fraction import convergents
@@ -712,7 +712,7 @@ def normalize(self):
             (1 + O(11^2), 2 + O(11))
         """
         sd = self._dict
-        for val in itervalues(sd):
+        for val in sd.values():
             val.normalize()
         return self
 
diff --git a/src/sage/modules/multi_filtered_vector_space.py b/src/sage/modules/multi_filtered_vector_space.py
index fd69bad8860..e7777d1b92a 100644
--- a/src/sage/modules/multi_filtered_vector_space.py
+++ b/src/sage/modules/multi_filtered_vector_space.py
@@ -38,7 +38,7 @@
 #  the License, or (at your option) any later version.
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-from six import iteritems, itervalues
+from six import iteritems
 
 from sage.rings.all import QQ, ZZ, Integer
 from sage.rings.infinity import infinity, minus_infinity
@@ -84,11 +84,11 @@ def MultiFilteredVectorSpace(arg, base_ring=None, check=True):
             base_ring = QQ
     else:
         filtration = dict(arg)
-        F = next(itervalues(arg))   # the first filtration
+        F = next(iter(arg.values()))  # the first filtration
         dim = F.dimension()
         if base_ring is None:
             base_ring = F.base_ring()
-    for deg in filtration.keys():
+    for deg in filtration:
         filt = filtration[deg]
         if filt.base_ring() != base_ring:
             filt = filt.change_ring(base_ring)
diff --git a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
index d404e0a76ba..710cbfba2e7 100644
--- a/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
+++ b/src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
@@ -63,7 +63,6 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 from __future__ import print_function, absolute_import
-from six import itervalues
 from six.moves import range
 
 from copy import copy
@@ -2087,12 +2086,12 @@ def __compute_via_velu(self, xP, yP):
         a3 = self.__E1.a3()
 
         # next iterate over the 2torsion points of the kernel
-        for Qvalues in itervalues(ker_2tor):
+        for Qvalues in ker_2tor.values():
             (tX, tY) = self.__velu_sum_helper(Qvalues, a1, a3, xP, yP)
             X = X + tX
             Y = Y + tY
 
-        for Qvalues in itervalues(ker_non2tor):
+        for Qvalues in ker_non2tor.values():
             (tX, tY) = self.__velu_sum_helper(Qvalues, a1, a3, xP, yP)
             X = X + tX
             Y = Y + tY
@@ -2158,11 +2157,11 @@ def __init_kernel_polynomial_velu(self):
 
         psi = poly_ring(1)
 
-        for Qvalues in itervalues(self.__kernel_2tor):
+        for Qvalues in self.__kernel_2tor.values():
             xQ = invX(x=Qvalues[0])
             psi = psi*(x - xQ)
 
-        for Qvalues in itervalues(self.__kernel_non2tor):
+        for Qvalues in self.__kernel_non2tor.values():
             xQ = invX(x=Qvalues[0])
             psi = psi*(x - xQ)
 
diff --git a/src/sage/sets/family.py b/src/sage/sets/family.py
index 5c2c72fae07..70e18002b2a 100644
--- a/src/sage/sets/family.py
+++ b/src/sage/sets/family.py
@@ -31,13 +31,12 @@
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-#                  http://www.gnu.org/licenses/
+#                  https://www.gnu.org/licenses/
 #*****************************************************************************
 import types
 from copy import copy
 from pprint import pformat, saferepr
 
-from six import itervalues
 from six.moves import range
 
 from sage.misc.cachefunc import cached_method
@@ -609,7 +608,7 @@ def values(self):
         if self._keys is not None:
             return [self._dictionary[key] for key in self._keys]
         else:
-            return list(itervalues(self._dictionary))
+            return list(self._dictionary.values())
 
     def has_key(self, k):
         """