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@@ -16,9 +16,9 @@ representations are themselves uniquely determined by the value of the trace, \\
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  where \\(g\\) ranges over subsets of \\(G\\) called conjugacy classes. These values are called *characters*.
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  The representation theory of symmetric groups has rich combinatorial interpretations. Both
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- irreducible representations of \\(S\_n\\) and the conjugacy classes of \\(S\_n\\) are indexed by
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- partitions of \\(n\\) and thus the characters of irreducible representations of \\(S\_n\\) are indexed
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- by pairs of partitions of \\(n\\). For \\(\lambda,\mu \vdash n\\) we write \\(\chi^\lambda\_\mu\\) for the
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  associated character. This combinatorial connection is not superficial, some of the most famous
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  algorithms for computation of irreducible characters (e.g., the
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  [Murnaghan-Nakayama rule](https://en.wikipedia.org/wiki/Murnaghan–Nakayama_rule)) are completely
 
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  where \\(g\\) ranges over subsets of \\(G\\) called conjugacy classes. These values are called *characters*.
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  The representation theory of symmetric groups has rich combinatorial interpretations. Both
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+ irreducible representations of \\(S_n\\) and the conjugacy classes of \\(S_n\\) are indexed by
20
+ partitions of \\(n\\) and thus the characters of irreducible representations of \\(S_n\\) are indexed
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+ by pairs of partitions of \\(n\\). For \\(\lambda,\mu \vdash n\\) we write \\(\chi^\lambda_\mu\\) for the
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  associated character. This combinatorial connection is not superficial, some of the most famous
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  algorithms for computation of irreducible characters (e.g., the
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  [Murnaghan-Nakayama rule](https://en.wikipedia.org/wiki/Murnaghan–Nakayama_rule)) are completely