id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
14542,Implement arithmetic product of cycle index series,agd,sage-combinat,"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]",enhancement,closed,major,sage-5.12,combinatorics,fixed,"species, cycle index",sage-combinat,sage-5.12.beta3,Andrew Gainer-Dewar,Darij Grinberg,N/A,,,,,