#14542: Implement arithmetic product of cycle index series
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Reporter: agd | Owner: sage-combinat
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-5.11
Component: combinatorics | Resolution:
Keywords: species, cycle index | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: u/agd/cis_arith_prod | Dependencies:
Stopgaps: |
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Description changed by darij:
Old description:
> In a 2008 paper (see below), Maia and Méndez define an operation on
> combinatorial species which they dub the "arithmetic product". This
> operation corresponds to a nice combinatorial operation: the arithmetic
> product F⊡G corresponds to the species of "F-assemblies of cloned
> G-structures", which are structures of the partitional composite species
> F∘G with the additional requirement that all the G-structures be
> isomorphic.
>
> As shown in the paper, the cycle index of the arithmetic product F⊡G can
> be computed in terms of the cycle indices of the species F and G. The
> attached patch adds code to calculate the result of this operation. It
> includes a doctest which verifies a nontrivial computation related to the
> species of "regular octopuses".
>
> * Maia, Manuel and Méndez, Miguel. On the arithmetic product of
> combinatorial species. 1 February 2008. http://arxiv.org/abs/math/0503436
>
> Apply [attachment:trac_14542_cycle_index_arithmetic_product.patch]
New description:
In a 2008 paper (see below), Maia and Méndez define an operation on
combinatorial species which they dub the "arithmetic product". This
operation corresponds to a nice combinatorial operation: the arithmetic
product F⊡G corresponds to the species of "F-assemblies of cloned
G-structures", which are structures of the partitional composite species
F∘G with the additional requirement that all the G-structures be
isomorphic.
As shown in the paper, the cycle index of the arithmetic product F⊡G can
be computed in terms of the cycle indices of the species F and G. The
attached patch adds code to calculate the result of this operation. It
includes a doctest which verifies a nontrivial computation related to the
species of "regular octopuses".
* Maia, Manuel and Méndez, Miguel. On the arithmetic product of
combinatorial species. 1 February 2008. http://arxiv.org/abs/math/0503436
Apply:
* [attachment:trac_14542_cycle_index_arithmetic_product.patch]
* [attachment:trac_14542-review-dg.patch]
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Ticket URL: <http://trac.sagemath.org/ticket/14542#comment:13>
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