BUG: Using `/` operator with a `Path` and `Series` of string dtype fails

[Dr-Irv]

Reproducible Example

import pandas as pd
from pathlib import Path
pd.options.future.infer_string = True  # Only needed with 2.3.1
folder = Path.cwd()
files = pd.Series(["a.png", "b.png"])
folder / files[0]   # This works
folder / files  # This raises an exception

Issue Description

The / operator with Path works fine with 2.3.1 with strings being object dtype, but not with arrow strings. The last statement produces this stacktrace:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\ops\common.py", line 76, in new_method
    return method(self, other)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arraylike.py", line 214, in __rtruediv__
    return self._arith_method(other, roperator.rtruediv)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\series.py", line 6146, in _arith_method
    return base.IndexOpsMixin._arith_method(self, other, op)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\base.py", line 1391, in _arith_method
    result = ops.arithmetic_op(lvalues, rvalues, op)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\ops\array_ops.py", line 273, in arithmetic_op
    res_values = op(left, right)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\roperator.py", line 27, in rtruediv
    return right / left
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\ops\common.py", line 76, in new_method
    return method(self, other)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arraylike.py", line 214, in __rtruediv__
    return self._arith_method(other, roperator.rtruediv)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arrays\arrow\array.py", line 836, in _arith_method
    return self._evaluate_op_method(other, op, ARROW_ARITHMETIC_FUNCS)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arrays\arrow\array.py", line 768, in _evaluate_op_method
    other = self._box_pa(other)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arrays\arrow\array.py", line 407, in _box_pa
    return cls._box_pa_scalar(value, pa_type)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arrays\string_arrow.py", line 154, in _box_pa_scalar
    pa_scalar = super()._box_pa_scalar(value, pa_type)
  File "C:\Condadirs\envs\pandasstubs\lib\site-packages\pandas\core\arrays\arrow\array.py", line 443, in _box_pa_scalar
    pa_scalar = pa.scalar(value, type=pa_type, from_pandas=True)
  File "pyarrow\\scalar.pxi", line 1670, in pyarrow.lib.scalar
  File "pyarrow\\error.pxi", line 155, in pyarrow.lib.pyarrow_internal_check_status
  File "pyarrow\\error.pxi", line 92, in pyarrow.lib.check_status
pyarrow.lib.ArrowInvalid: Could not convert WindowsPath('c:/Code/pandas-stubs') with type WindowsPath: did not recognize Python value type when inferring an Arrow data type

While the error says something about Windows, a similar error occurs in Linux.

Expected Behavior

No exception thrown

Installed Versions

INSTALLED VERSIONS

commit : c888af6
python : 3.10.14
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.26100
machine : AMD64
processor : Intel64 Family 6 Model 183 Stepping 1, GenuineIntel
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United States.1252

pandas : 2.3.1
numpy : 2.2.6
pytz : 2025.2
dateutil : 2.9.0.post0
pip : 24.2
Cython : None
sphinx : None
IPython : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.4
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : 1.1
hypothesis : None
gcsfs : None
jinja2 : 3.1.6
lxml.etree : 6.0.0
matplotlib : 3.10.3
numba : None
numexpr : 2.11.0
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 21.0.0
pyreadstat : 1.3.0
pytest : 8.4.1
python-calamine : None
pyxlsb : 1.0.10
s3fs : None
scipy : 1.15.3
sqlalchemy : 2.0.41
tables : 3.10.1
tabulate : 0.9.0
xarray : 2025.6.1
xlrd : 2.0.2
xlsxwriter : 3.2.5
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None

[jorisvandenbossche]

This is not actually specific to pyarrow, also with the object-backed string dtype this does not work, so this is a general issue of supporting / (__truediv__) for the string dtype.

>>> folder = Path.cwd()
>>> files = pd.Series(["a.png", "b.png"], dtype=pd.StringDtype("python", na_value=np.nan))
>>> folder / files
...
File ~/scipy/repos/pandas/pandas/core/arraylike.py:217, in OpsMixin.__rtruediv__(self, other)
    215 @unpack_zerodim_and_defer("__rtruediv__")
    216 def __rtruediv__(self, other):
--> 217     return self._arith_method(other, roperator.rtruediv)

File ~/scipy/repos/pandas/pandas/core/arrays/string_.py:1057, in StringArray._cmp_method(self, other, op)
   1054 valid = ~mask
   1056 if not lib.is_scalar(other):
-> 1057     if len(other) != len(self):
   1058         # prevent improper broadcasting when other is 2D
   1059         raise ValueError(
   1060             f"Lengths of operands do not match: {len(self)} != {len(other)}"
   1061         )
   1063     # for array-likes, first filter out NAs before converting to numpy

TypeError: object of type 'PosixPath' has no len()

For object dtype this works, because in that case we just defer calling the operation on the individual objects, and then str will defer to Path to handle it.
So I think the question is if we want to support this specific case of / for string dtype (I am fine with that, as this seems a useful use case)

[Dr-Irv]

So I think the question is if we want to support this specific case of / for string dtype (I am fine with that, as this seems a useful use case)

It was reported with pandas-stubs at pandas-dev/pandas-stubs#682 (so people are doing it) and added to the tests there, which is how I uncovered this issue with the new StringDtype.