=========================== k_combinat_for_sage

k-Schur and other "k-math-objects" for combinatorics. This code is meant to be used with SageMath <https://www.sagemath.org/>, and parts of it have already been migrated <https://github.com/sagemath/sage/issues/25931> into SageMath itself. The functions in the code come from research by Jennifer Morse <http://math.virginia.edu/people/jlm6cj/>_ and her colleagues. You will see in the documentation references to various research papers, which are the relevant topics.

Quicklinks

• documentation <https://mareoraft.github.io/k_combinat_for_sage/>_
• proof of work <https://github.com/MareoRaft/k_combinat_for_sage/blob/master/k_combinat_for_sage/proof_of_work.py>_

Contents

This code computes combinatorial things such as

• k-boundaries
• k-rim
• k-shape partitions
• skew-linked diagrams
• k-irreducible partitions
• irreducible k-shapes
• root ideals
• raising root operators
• catalan functions
• dual symmetric functions
• double symmetric functions

etc. For a full list of functions, read the documentation.

Install or upgrade

::

$ sage -pip install --upgrade k_combinat_for_sage

If you get an SSL error, you can download the latest version manually at PyPI <https://pypi.org/project/k-combinat-for-sage/#files> and then install/upgrade with :code:sage -pip install --upgrade /path/to/downloaded/file. If you want to fix the SSL issue permanently, look here <https://ask.sagemath.org/question/38746/sage-pip-not-compatible-with-pypi/>.

Usage

Put your code in a file such as myscript.py. Import all the functions with::

from k_combinat_for_sage.all import *

and then use functions at will, such as::

p = Partition([4, 3, 3, 1])
if is_symmetric(p):
    print("it's symmetric, boogie woogie woogie!")

Finally, you can run your file with sage::

$ sage myscript.py
it's symmetric, boogie woogie woogie!