# Revision history [back]

### orderedsetpartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like NULL,NULL,[1,2,3,4,5] or NULL,[1,2,3],[4,5] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

### orderedsetpartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like NULL,NULL,[1,2,3,4,5] or NULL,[1,2,3],[4,5] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


### orderedsetpartitions OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like NULL,NULL,[1,2,3,4,5] [],[],[1,2,3,4,5] or NULL,[1,2,3],[4,5] [],[1,2,3],[4,5] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [],[],[1,2,3,4,5] or [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
print("res=")
print(res)
count=count+1
return(truc)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine,

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
print("res=")
print(res)
count=count+1
return(truc)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine, fine when coding, but somehow res seems to be "None" instead of []

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
print("res=")
print(res)
count=count+1
return(truc)
return(res)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine when coding, but somehow res seems to be "None" instead of []

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
#  res=res.append([tmp]) # tried this too
print("res=")
print(res)
count=count+1
return(res)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine when coding, but somehow res seems to be "None" instead of []

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


The problem is about res if i omit the line res=res.append(tmp), i will get the enumeration ok i think

### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
#  res=res.append([tmp]) # tried this too
print("res=")
print(res)
count=count+1
return(res)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine when coding, but somehow res seems to be "None" instead of []

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


The problem is about res if i omit the line res=res.append(tmp), i will get the enumeration ok i think

EDIT: i changed res=res.append(tmp) by res.append(tmp) i also changed the line initializing tmp into tmp=[ set() for i in range(k)] now as a result of print(tmp) i get the correct enumeration

[{0, 1, 2}, set([]), set([])]
[set([]), {0, 1, 2}, set([])]
[set([]), set([]), {0, 1, 2}]
[{0, 1}, {2}, set([])]
[{0, 2}, {1}, set([])]
[{1, 2}, {0}, set([])]
[{0}, {1, 2}, set([])]
[{1}, {0, 2}, set([])]
[{2}, {0, 1}, set([])]
[{0, 1}, set([]), {2}]
[{0, 2}, set([]), {1}]
[{1, 2}, set([]), {0}]
[{0}, set([]), {1, 2}]
[{1}, set([]), {0, 2}]
[{2}, set([]), {0, 1}]
[set([]), {0, 1}, {2}]
[set([]), {0, 2}, {1}]
[set([]), {1, 2}, {0}]
[set([]), {0}, {1, 2}]
[set([]), {1}, {0, 2}]
[set([]), {2}, {0, 1}]
[{0}, {1}, {2}]
[{0}, {2}, {1}]
[{1}, {0}, {2}]
[{2}, {0}, {1}]
[{1}, {2}, {0}]
[{2}, {1}, {0}]


However, for res, i get the strange result

[[{0, 1, 2}, set(), set()],
[set(), {0, 1, 2}, set()],
[set(), set(), {0, 1, 2}],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}]]


only the first 3 lines are correct. There seems to be some side-effects. This is very enigmatic to me because between print(tmp) and res.append(tmp) there are no instructions at all !!!!

### OrderedSetPartitions (variant)

I would like to have the list of partitions of [1,2,...N] of finite size k but with using the NULL set

for example, if looking for the partitions of [1,2,3,4,5] of size 3, i would like [ [],[],[1,2,3,4,5] ]

and [ [],[1,2,3],[4,5] ] to be in this list

is it possible to do natively in Sage, or should i write a custom function ?

OrderedSetPartitions(5,3).list()

returns

[[{1, 2, 3}, {4}, {5}],
[{1, 2, 3}, {5}, {4}],
[{1, 2, 4}, {3}, {5}],
[{1, 2, 5}, {3}, {4}],...


EDIT: here is a (non optimized at all) attempt to solve naively this problem

def OrderedSetPartitions_0(A,k):

cols={i for i in range(k)}
# returns the list of k-OrderedSetPartitions of A, allowing for the empty set
s=Subsets(cols).list()
res=[]
count=0
P=[OrderedSetPartitions(A,i) for i in range(k+1)]

for sub in s:
print("sub=")
print(sub)

tmp=[ {} for i in range(k)]
c=sub.cardinality()
for part in P[c]:
print("part=")
print(part)
for i in range(c):
tmp[sub[i]]=part[i]

print("tmp=")
print(tmp)

res=res.append([tmp])
#  res=res.append([tmp]) # tried this too
print("res=")
print(res)
count=count+1
return(res)
# print(count)

A=range(3)
k=2
A
P=[OrderedSetPartitions(A,i) for i in range(k+1)]
# note that P[2].list is a list of list !
P[2].list()

[[{0, 1}, {2}],
[{0, 2}, {1}],
[{1, 2}, {0}],
[{0}, {1, 2}],
[{1}, {0, 2}],
[{2}, {0, 1}]]

myset=OrderedSetPartitions_0(A,k)


I get this error message, and I admit I don't get it at all, because it looks fine when coding, but somehow res seems to be "None" instead of []

sub=
{}
sub=
{0}
part=
[{0, 1, 2}]
tmp=
[{0, 1, 2}, {}]
res=
None
sub=
{1}
part=
[{0, 1, 2}]
tmp=
[{}, {0, 1, 2}]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_21.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("#


-- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("bXlzZXQ9T3JkZXJlZFNldFBhcnRpdGlvbnNfMChBLGsp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

  File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpryfYOj/___code___.py", line 2, in <module>
exec compile(u'myset=OrderedSetPartitions_0(A,k)
File "", line 1, in <module>

File "/private/var/folders/gm/z065gk616xg6g0xgn4c7_bvc0000gn/T/tmpSH_9LF/___code___.py", line 27, in OrderedSetPartitions_0
res=res.append([tmp])
AttributeError: 'NoneType' object has no attribute 'append'


The problem is about res if i omit the line res=res.append(tmp), i will get the enumeration ok i think

EDIT: i changed res=res.append(tmp) by res.append(tmp) i also changed the line initializing tmp into tmp=[ set() for i in range(k)] now as a result of print(tmp) i get the correct enumeration

[{0, 1, 2}, set([]), set([])]
[set([]), {0, 1, 2}, set([])]
[set([]), set([]), {0, 1, 2}]
[{0, 1}, {2}, set([])]
[{0, 2}, {1}, set([])]
[{1, 2}, {0}, set([])]
[{0}, {1, 2}, set([])]
[{1}, {0, 2}, set([])]
[{2}, {0, 1}, set([])]
[{0, 1}, set([]), {2}]
[{0, 2}, set([]), {1}]
[{1, 2}, set([]), {0}]
[{0}, set([]), {1, 2}]
[{1}, set([]), {0, 2}]
[{2}, set([]), {0, 1}]
[set([]), {0, 1}, {2}]
[set([]), {0, 2}, {1}]
[set([]), {1, 2}, {0}]
[set([]), {0}, {1, 2}]
[set([]), {1}, {0, 2}]
[set([]), {2}, {0, 1}]
[{0}, {1}, {2}]
[{0}, {2}, {1}]
[{1}, {0}, {2}]
[{2}, {0}, {1}]
[{1}, {2}, {0}]
[{2}, {1}, {0}]


However, for res, i get the strange result

[[{0, 1, 2}, set(), set()],
[set(), {0, 1, 2}, set()],
[set(), set(), {0, 1, 2}],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, {0, 1}, set()],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[{2}, set(), {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[set(), {2}, {0, 1}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}],
[{2}, {1}, {0}]]


only the first 3 lines are correct. There seems to be some side-effects. This is very enigmatic to me because between print(tmp) and res.append(tmp) there are no instructions at all !!!!