Abstract
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.
Original language | English (US) |
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Pages (from-to) | 281-298 |
Number of pages | 18 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 109 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2005 |
Keywords
- Binomial coefficients
- Determinant evaluations
- Non-intersecting lattice paths
- Symmetric functions
- Symmetric group
- m-quasiinvariants