Update README.md

README.md

@@ -32,15 +32,15 @@ The model operates on a compact word-level vocabulary for permutation syntax. Tr
 
 ## Training Data
 
-PermuFormer was trained autoregressively on synthetic permutation examples generated with exact combinatorial algorithms. The paper describes a dataset of 39.8M instances, approximately 2.66B tokens, over the symmetric groups $S_2$ through `S_11`.
+PermuFormer was trained autoregressively on synthetic permutation examples generated with exact combinatorial algorithms. The paper describes a dataset of 39.8M instances, approximately 2.66B tokens, over the symmetric groups `S_2` through `S_11`.
 
 Training tasks cover three broad families:
 
-- **Translation between encodings:** one-line notation, cycle notation, reduced Coxeter expressions, RSK tableaux, inversion vectors, and Lehmer codes.
-- **Permutation statistics and properties:** length, descents, fixed points, sign/parity, cycle type, RSK shape, pattern avoidance, longest increasing/decreasing subsequences, and related statistics.
-- **Algebraic operations and comparisons:** product/composition, inverse, powers, conjugation, commutator, relative products, multiplication by simple transpositions, complement, reverse, descent tests, and Bruhat order.
+- **Translation between encodings:** One-line notation, cycle notation, reduced Coxeter expressions, RSK tableaux, inversion vectors, and Lehmer codes.
+- **Permutation statistics and properties:** Length, descents, fixed points, sign/parity, cycle type, RSK shape, pattern avoidance, longest increasing/decreasing subsequences, and related statistics.
+- **Algebraic operations and comparisons:** Product/composition, inverse, powers, conjugation, commutator, relative products, multiplication by simple transpositions, complement, reverse, descent tests, and Bruhat order.
 
-Some targets include computational witnesses before the final answer, for example inversion lists before a length answer or pattern witnesses before an avoidance answer.
+Some targets include computational witnesses before the final answer, for example inversions are listed before a computation of length. Similarly pattern witnesses are stated before an avoidance answer.
 
 ## Usage