# TypeError: unhashable type: 'list' in constructing poset

I have the following code to generate all multiset partitions of a given multiset (list).

```
k0 = 2
k1 = 1
k2 = 1
#k3 = 1
l = k0+k1+k2 #+k3
L = [ ]
for i in range(k0) :
L.append(0)
for i in range(k1) :
L.append(1)
for i in range(k2) :
L.append(2)
print L
#L = [0,1,2,3]
LL = list(range(len(L)))
print LL
P = SetPartitions(LL)
P = list(P)
J = []
for p in P :
J.append([])
aa = P.index(p)
for i in p :
J[aa].append(list(i))
#print J
JJ =[]
for j in J :
JJ.append([])
bb = J.index(j)
for i in j :
JJ[bb].append([])
aa = j.index(i)
for k in i :
#print aa
JJ[bb][aa].append(L[k])
print JJ
```

The above code gives me the following output

```
[0, 0, 1, 2]
[0, 1, 2, 3]
[[[0, 0, 1, 2]], [[0], [0, 1, 2]], [[0, 1, 2], [0]], [[0, 0, 2], [1]], [[0, 0, 1], [2]], [[0, 0], [1, 2]], [[0, 1], [0, 2]], [[0, 2], [0, 1]], [[0], [0], [1, 2]], [[0], [0, 2], [1]], [[0], [0, 1], [2]], [[0, 2], [0], [1]], [[0, 1], [0], [2]], [[0, 0], [1], [2]], [[0], [0], [1], [2]]]
```

I have the following code to generate a poset out of JJ in which the order is given by the refinement.

```
sage: elms = JJ
sage: def fcn(A, B):
....: if len(A) != len(B) + 1:
....: return False
....: for a in A:
....: if not any(set(a).issubset(b) for b in B):
....: return False
....: return True
sage: Poset((elms, fcn), cover_relations=True)
```

I usually work with sets and my input JJ is usually a set partition and the program works well.

Now, I am working with multisets (like [0,1,1,2,2,2,2]) and multi partitions (like [[0],[1,2],[1,2],[2,2]). By a multi-partition, I mean a partition in which each part is a multiset and parts can be repeated in a partition. So basically it is a list of lists. We cannot implement this using sets. I have codes given above to generate all such partitions in sage using lists.

Now, the set of all multi partitions JJ (which is implements as a list) of a multiset (which is also implemented as a list) has to be fed as an input to the above code to generate the poset. But the above code throws the error

```
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-42-993ec557f50c> in <module>()
7 return False
8 return True
----> 9 Poset((elms, fcn), cover_relations=True)
/Applications/SageMath-8.1.app/Contents/Resources/sage/local/lib/python2.7/site-packages/sage/combinat/posets/posets.pyc in Poset(data, element_labels, cover_relations, linear_extension, category, facade, key)
674 raise TypeError("not a list of relations")
675 D = DiGraph()
--> 676 D.add_vertices(elements)
677 D.add_edges(relations, loops=False)
678 elif len(data) > 2:
/Applications/SageMath-8.1.app/Contents/Resources/sage/local/lib/python2.7/site-packages/sage/graphs/generic_graph.pyc in add_vertices(self, vertices)
9602
9603 """
-> 9604 return self._backend.add_vertices(vertices)
9605
9606 def delete_vertex(self, vertex, in_order=False):
/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.add_vertices (build/cythonized/sage/graphs/base/c_graph.c:14020)()
1504 for v in vertices:
1505 if v is not None:
-> 1506 self.add_vertex(v)
1507 else:
1508 nones += 1
/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.add_vertex (build/cythonized/sage/graphs/base/c_graph.c:13856)()
1454 retval = name
1455
-> 1456 self.check_labelled_vertex(name,
1457 (self._directed and
1458 self._cg_rev is not None)) # this will add the vertex
/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.check_labelled_vertex (build/cythonized/sage/graphs/base/c_graph.c:12310)()
1153 cdef CGraph G_rev = self._cg_rev
1154
-> 1155 cdef int u_int = self.get_vertex(u)
1156 if u_int != -1:
1157 if not bitset_in(G.active_vertices, u_int):
/Applications/SageMath-8.1.app/Contents/Resources/sage/src/sage/graphs/base/c_graph.pyx in sage.graphs.base.c_graph.CGraphBackend.get_vertex (build/cythonized/sage/graphs/base/c_graph.c:11902)()
1120 cdef CGraph G = self._cg
1121 cdef long u_long
-> 1122 if u in vertex_ints:
1123 return vertex_ints[u]
1124 try:
TypeError: unhashable type: 'list'
```

How to overcome this issue? Kindly help me with this. Thank you.

Please provide a sequence of commands one can run to get the same error.

Could not obtain the same error, trying

`M = [0, 1, 1, 2, 2, 2, 2]`

followed by the code in the question`M = [[0], [1, 2], [1, 2], [2, 2]]`

followed by the code in the question@slelievre I have added the full code. Kindly check. Thank you. I directly feed M = [[0], [1, 2], [1, 2], [2, 2]] but it is throwing the same error message.

Suggestion : use tuples (and sort them) instead of lists.