#14846: CycleIndexSeries derivative, integral, exponential methods are not
combinatorial
-------------------------------------+-------------------------------------
Reporter: agd | Owner: agd
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-6.8
Component: combinatorics | Resolution:
Keywords: LazyPowerSeries, | Merged in:
species | Reviewers: Martin Rubey
Authors: Andrew Gainer- | Work issues: documentation
Dewar | Commit:
Report Upstream: N/A | ab9c7d161b8318bc5edffb3bb3dd66bc5c503318
Branch: u/agd/cis/deriv | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by mantepse):
* status: needs_review => positive_review
Comment:
I played with the code and the examples, and found myself happy. For
example,
{{{
sage: T = CombinatorialSpecies()
sage: X = species.SingletonSpecies()
sage: E = species.SetSpecies()
sage: T.define(X*E(T))
sage: s = T.cycle_index_series()
sage: oeis(s.logarithm().generating_series().counts(12))
0: A133297: a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*n^(n-k-1)/(n-k)!.
sage: oeis(s.pointing().generating_series().counts(12)[1:])
0: A000312: Number of labeled mappings from n points to themselves
(endofunctions): n^n.
1: A177885: (1-n)^(n-1).
2: A086783: Discriminant of the polynomial x^n - 1.
sage: oeis(s.pointing().isotype_generating_series().counts(12)[1:])
0: A000107: Number of rooted trees with n nodes and a single labeled node;
pointed rooted trees; vertebrates.
}}}
Thanks for the code and thanks for the patience!
--
Ticket URL: <http://trac.sagemath.org/ticket/14846#comment:37>
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