There are plenty of polynomials, and only a few are specializations of Macdonald polynomials. As a polynomial botanist, the following is a very incomplete family tree.


[![polynomials][1]][1]

Edit: I added a few more generalizations, but it is getting crowded. Click on the image for a larger version.

[![bigger graph][2]][2]


  [1]: https://i.sstatic.net/g5925.png
  [2]: https://i.sstatic.net/PS9jA.png