Define the class of SuperPartitions

[zabrocki]

These combinatorial objects index the space of symmetric polynomials in
two sets of variables, one commuting and one anti-commuting, and they
are known as symmetric functions in super space (hence the origin of the
name super partitions).

Super partitions may be input in two different formats: one as a pair
consisiting of fermionic (strict partition) and a bosonic (partition) part
and as a list of integer values where the negative entries come first
and are listed in strict order followed by the positive values in weakly
decreasing order.

A super partition is displayed as two partitions separated by a semicolon
as a default. Super partitions may also be displayed as a weakly increasing
sequence of integers that are strict if the numbers are not positive.

CC: @tscrim @alauve @darijgr

Component: combinatorics

Keywords: IMA coding sprint, CHAs

Author: Mike Zabrocki

Branch/Commit: c83f8da

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/25132

[tscrim]

Changed keywords from IMA coding sprint, combinatorics combinatorics, Hopf algebras to IMA coding sprint, CHAs

[sagetrac-git]

Changed commit from d41f19c to de0f90b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

de0f90b

doc changes and rename one pieri rule

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

139b594

add superpartition to the doc

[sagetrac-git]

Changed commit from de0f90b to 139b594

[sagetrac-git]

Changed commit from 139b594 to 0e7c0c9

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

0e7c0c9

doc corrections, added to list of catalog_partitions and enumerated_sets, pyflakes

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

89a1764

Refactored class to use ClonableArray. Other reviewer changes.

[sagetrac-git]

Changed commit from 0e7c0c9 to 89a1764

[tscrim]

comment:7

If my changes are good, then positive review. Thank you.

[tscrim]

Reviewer: Travis Scrimshaw

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c83f8da

corrected reference

[sagetrac-git]

Changed commit from 89a1764 to c83f8da

[zabrocki]

comment:9

Looks good. Thanks for the review.

[zabrocki]

comment:10

Note: #25163 is the follow up ticket and the reason for implementing this object.

[vbraun]

Changed branch from public/superpartitions to c83f8da