#14906: Implement method to expand cycle index series as symmetric function in
variables
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Reporter: agd | Owner: agd
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.12
Component: combinatorics | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Andrew Gainer-Dewar
Merged in: | Dependencies:
Stopgaps: |
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The cycle index series of a species is a symmetric function in the power-
sum basis. Expanding this symmetric function in a set of underlying
variables can reveal interesting enumerative information about the
species; the coefficients of this underlying power series count
"partially-labeled" structures in a Pólya-theoretic sense.
The attached patch adds an ``expand_as_sf`` method to the
``CycleIndexSeries`` class which performs this expansion. It essentially
just calls the ``expand`` method of the underlying symmetric functions,
then uses the result as the terms of a ``LazyPowerSeries``.
This code is doctested and ready for review.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14906>
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