BUG: to_string truncation column with index=False (#40907)

Author: mikeronayne

doc/source/whatsnew/v1.3.0.rst

@@ -750,6 +750,7 @@ I/O
 - Bug in :func:`read_hdf` returning unexpected records when filtering on categorical string columns using ``where`` parameter (:issue:`39189`)
 - Bug in :func:`read_sas` raising ``ValueError`` when ``datetimes`` were null (:issue:`39725`)
 - Bug in :func:`read_excel` dropping empty values from single-column spreadsheets (:issue:`39808`)
+- Bug in :meth:`DataFrame.to_string` misplacing the truncation column when ``index=False`` (:issue:`40907`)
 
 Period
 ^^^^^^

pandas/io/formats/string.py

@@ -77,7 +77,8 @@ def _insert_dot_separators(self, strcols: List[List[str]]) -> List[List[str]]:
     def _insert_dot_separator_horizontal(
         self, strcols: List[List[str]], index_length: int
     ) -> List[List[str]]:
-        strcols.insert(self.fmt.tr_col_num + 1, [" ..."] * index_length)
+        tr_col_num = self.fmt.tr_col_num + 1 if self.fmt.index else self.fmt.tr_col_num
+        strcols.insert(tr_col_num, [" ..."] * index_length)
         return strcols
 
     def _insert_dot_separator_vertical(

pandas/tests/io/formats/test_to_string.py

@@ -106,6 +106,40 @@ def test_format_remove_leading_space_dataframe(input_array, expected):
     assert df == expected
 
 
+@pytest.mark.parametrize(
+    "max_cols, expected",
+    [
+        (
+            10,
+            [
+                " 0   1   2   3   4   ...  6   7   8   9   10",
+                "  0   0   0   0   0  ...   0   0   0   0   0",
+                "  0   0   0   0   0  ...   0   0   0   0   0",
+            ],
+        ),
+        (
+            9,
+            [
+                " 0   1   2   3   ...  7   8   9   10",
+                "  0   0   0   0  ...   0   0   0   0",
+                "  0   0   0   0  ...   0   0   0   0",
+            ],
+        ),
+        (
+            1,
+            [
+                " 0  ...",
+                " 0  ...",
+                " 0  ...",
+            ],
+        ),
+    ],
+)
+def test_truncation_col_placement_no_index(max_cols, expected):
+    df = DataFrame([[0] * 11] * 2)
+    assert df.to_string(index=False, max_cols=max_cols).split("\n") == expected
+
+
 def test_to_string_unicode_columns(float_frame):
     df = DataFrame({"\u03c3": np.arange(10.0)})