.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/combinatorics/partitions/plot_01_partitions_and_young_diagrams.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_combinatorics_partitions_plot_01_partitions_and_young_diagrams.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_combinatorics_partitions_plot_01_partitions_and_young_diagrams.py:


Integer partitions, the partition function, and Young diagrams
======================================================================

Enumerates every partition of 6, checks the count against the
partition function ``p(6)``, and visualizes one partition's Young
diagram and its conjugate.

.. GENERATED FROM PYTHON SOURCE LINES 11-14

.. code-block:: Python

    from mathematicskit.combinatorics import YoungDiagram, integer_partitions, partition_function
    from mathematicskit.combinatorics.visualizers.plots import plot_partition_counts, plot_young_diagram








.. GENERATED FROM PYTHON SOURCE LINES 15-17

Enumerate the partitions of 6
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 17-23

.. code-block:: Python


    partitions = integer_partitions(6)
    print(f"p(6) = {partition_function(6)}, enumerated {len(partitions)} partitions:")
    for p in partitions:
        print(" ", p)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    p(6) = 11, enumerated 11 partitions:
      [6]
      [5, 1]
      [4, 2]
      [4, 1, 1]
      [3, 3]
      [3, 2, 1]
      [3, 1, 1, 1]
      [2, 2, 2]
      [2, 2, 1, 1]
      [2, 1, 1, 1, 1]
      [1, 1, 1, 1, 1, 1]




.. GENERATED FROM PYTHON SOURCE LINES 24-26

A Young diagram and its conjugate
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-34

.. code-block:: Python


    diagram = YoungDiagram([4, 2, 1])
    print("\nFerrers diagram of (4, 2, 1):")
    print(diagram.ferrers_diagram())
    print("conjugate partition:", diagram.conjugate().parts)

    plot_young_diagram(diagram)




.. image-sg:: /api/gallery/combinatorics/partitions/images/sphx_glr_plot_01_partitions_and_young_diagrams_001.png
   :alt: Young diagram of [4, 2, 1]
   :srcset: /api/gallery/combinatorics/partitions/images/sphx_glr_plot_01_partitions_and_young_diagrams_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Ferrers diagram of (4, 2, 1):
    ****
    **
    *
    conjugate partition: [3, 2, 1, 1]

    <Axes: title={'center': 'Young diagram of [4, 2, 1]'}>



.. GENERATED FROM PYTHON SOURCE LINES 35-37

Growth of the partition function
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 37-39

.. code-block:: Python


    plot_partition_counts(30)



.. image-sg:: /api/gallery/combinatorics/partitions/images/sphx_glr_plot_01_partitions_and_young_diagrams_002.png
   :alt: Integer partition function
   :srcset: /api/gallery/combinatorics/partitions/images/sphx_glr_plot_01_partitions_and_young_diagrams_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <Axes: title={'center': 'Integer partition function'}, xlabel='n', ylabel='p(n)'>




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.042 seconds)


.. _sphx_glr_download_api_gallery_combinatorics_partitions_plot_01_partitions_and_young_diagrams.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_partitions_and_young_diagrams.ipynb <plot_01_partitions_and_young_diagrams.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_partitions_and_young_diagrams.py <plot_01_partitions_and_young_diagrams.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_partitions_and_young_diagrams.zip <plot_01_partitions_and_young_diagrams.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_