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. [A more comprehensive list of symmetric functions and generalizations can be found here.][1] [![polynomials][2]][2] Edit: I added a few more generalizations, but it is getting crowded. Click on the image for a larger version. [![bigger graph][3]][3] [1]: https://www.math.upenn.edu/~peal/polynomials/polynomialindex.htm [2]: https://i.sstatic.net/g5925.png [3]: https://i.sstatic.net/PS9jA.png