fixed_by(g), a tensor power to its section fixed by g, a permutation of the positions after a letter map on every letter: an arrow between tensors. By Pólya each cycle of g fills with the letters it fixes, at most \(|\Sigma|^{\ell}\) for a cycle of length \(\ell\), so the section's density is at most 1. The section is the equalizer \(\mathrm{Eq}(\mathrm{id}, g)\) (IsEqualizer, :pullback), equally the limit of the action of \(\langle g \rangle\) on the power, a functor out of its delooping (ActionFunctor, Delooping, :functor): its invariants, Pólya their count.
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Public Types | |
| using | Domain = P |
| using | Codomain = Symmetric<P, S, T> |
Public Member Functions | |
| constexpr Codomain | operator() (const P &p) const |
Public Attributes | |
| S | sigma |
| T | tau |
Detailed Description
struct dedekind::category::FixedBy< P, S, T >
fixed_by(g), a tensor power to its section fixed by g, a permutation of the positions after a letter map on every letter: an arrow between tensors. By Pólya each cycle of g fills with the letters it fixes, at most \(|\Sigma|^{\ell}\) for a cycle of length \(\ell\), so the section's density is at most 1. The section is the equalizer \(\mathrm{Eq}(\mathrm{id}, g)\) (IsEqualizer, :pullback), equally the limit of the action of \(\langle g \rangle\) on the power, a functor out of its delooping (ActionFunctor, Delooping, :functor): its invariants, Pólya their count.
- Template Parameters
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P the power. S the permutation. T the map.
The documentation for this struct was generated from the following file:
- src/main/modules/dedekind/category/periodic.cppm
