.. _sphx_glr_api_gallery_abstract_algebra_actions:

Group actions
-------------

Orbits of a group acting on a finite set, and Burnside's orbit-counting
lemma.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Counts two-colored necklaces (up to rotation) and bracelets (up to rotation and reflection) by averaging fixed points, and checks each count against direct orbit enumeration.">

.. only:: html

  .. image:: /api/gallery/abstract_algebra/actions/images/thumb/sphx_glr_plot_01_burnside_necklaces_thumb.png
    :alt:

  :doc:`/api/gallery/abstract_algebra/actions/plot_01_burnside_necklaces`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Burnside's lemma: counting necklaces</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/abstract_algebra/actions/plot_01_burnside_necklaces