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authorUlli Kehrle <ulli.kehrle@rwth-aachen.de>2018-11-08 12:04:47 +0100
committerUlli Kehrle <ulli.kehrle@rwth-aachen.de>2018-11-08 12:04:47 +0100
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downloadsubgroup-ladders-407bc6af406de7286d377e5f2d1f848aaa84eb2e.tar.gz
subgroup-ladders-407bc6af406de7286d377e5f2d1f848aaa84eb2e.tar.xz
use unicode subscripts
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@@ -5,11 +5,11 @@ The algorithm was described by Bernd Schmalz in [1, Theorem 3.1.1].
Solutions of some problems in group theory can relatively easy be transferred to a sub- or supergroup if the index is small.
Let G be a permutation group on the set {1,…,n}.
-So one might try to find a series of subgroups G = H_0,…,H_k = S_n of the symmetric group S_n such that H_{i-1} is a subgroup of H_i for every i and transfer the solution of a problem for the symmetric group step by step to G.
+So one might try to find a series of subgroups G = H₀,…,Hₖ = Sₙ of the symmetric group Sₙsuch that Hᵢ₋₁ is a subgroup of Hᵢfor every i and transfer the solution of a problem for the symmetric group step by step to G.
Sometimes it is not possible to find such a series with small indices between consecutive subgroups.
This is where subgroup ladders may make sense:
-A subgroup ladder is series of subgroups G = H_0,…,H_k = S_n of the symmetric group such that for every 1≤i≤k, H_i is a subgroup of H_{i-1} or H_{i-1} is a subgroup of H_i.
+A subgroup ladder is series of subgroups G = H₀,…,Hₖ = Sₙ of the symmetric group such that for every 1≤i≤k, Hᵢ is a subgroup of Hᵢ₋₁ or Hᵢ₋₁ is a subgroup of Hᵢ.
So we sometimes go up to a larger group in order to keep the indices small.
If G is a Young subgroup of S_n, the algorithm in this repository can find a subgroup ladder of G such that the indices are at most the degree of the permutation group.
@@ -38,7 +38,7 @@ A subgroup ladder may look like this:
|
|
H_0 = G
-```.
+```
TODO: add a description of your package; perhaps also instructions how how to