diff --git a/parity_tensor/parity_tensor.py b/parity_tensor/parity_tensor.py
index 15612ff..38c7332 100644
--- a/parity_tensor/parity_tensor.py
+++ b/parity_tensor/parity_tensor.py
@@ -63,6 +63,35 @@ def update_mask(self) -> ParityTensor:
         self._tensor = torch.where(self.mask, self._tensor, 0)
         return self
 
+    def permute(self, before_by_after: tuple[int, ...]) -> ParityTensor:
+        """
+        Permute the indices of the parity tensor.
+        """
+        assert set(before_by_after) == set(range(self.tensor.dim())), "Permutation indices must cover all dimensions."
+
+        edges = tuple(self.edges[i] for i in before_by_after)
+        tensor = self.tensor.permute(before_by_after)
+        parity = tuple(self.parity[i] for i in before_by_after)
+        mask = self.mask.permute(before_by_after)
+
+        total_parity = functools.reduce(
+            torch.logical_xor,
+            (
+                torch.logical_and(parity[i], parity[j])
+                for j in range(self.tensor.dim())
+                for i in range(0, j)  # all 0 <= i < j < dim
+                if before_by_after[i] > before_by_after[j]),
+            torch.zeros([], dtype=torch.bool),
+        )
+        tensor = torch.where(total_parity, -tensor, +tensor)
+
+        return ParityTensor(
+            _edges=edges,
+            _tensor=tensor,
+            _parity=parity,
+            _mask=mask,
+        )
+
     def __post_init__(self) -> None:
         assert len(self._edges) == self._tensor.dim(), f"Edges length ({len(self._edges)}) must match tensor dimensions ({self._tensor.dim()})."
         for dim, (even, odd) in zip(self._tensor.shape, self._edges):