Recursion and explicit formulas for particular \(N\)-variable Knop-Sahi and Macdonald polynomials (Q1806210)

The Knop-Sahi polynomials are non-homogemeous, non-symmetric polynomials for which the top homogeneous components are the non-symmetric Macdonald polynomials. The author finds an explicit formula for the Knop-Sahi polynomials indexed by the partition \((k,r^{n-1})\). An explicit formula for the corresponding nonsymmetric Macdonald polynomial is then a simple corollary. The method relies on a recursion for the Knop-Sahi that is based on the number of variables.