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