Let sij represent a transposition in Sn. A polynomial P in ℚ[Xn] is said to be m-quasiinvariant with respect to Sn if (χi - χj) 2m+1 divides (1 - sij) P for all 1 ≤ i, j ≤ n. We call the ring of m-quasiinvariants, QIm[Xn]. We describe a method for constructing a basis for the quotient QIm[X3]/(e1, e2, e3). This leads to the evaluation of certain binomial determinants that are interesting in their own right.
- Binomial coefficients
- Determinant evaluations
- Non-intersecting lattice paths
- Symmetric functions
- Symmetric group