Quasiinvariants of

Let s ij represent a transposition in S n . A polynomial P in Q [ X n ] is said to be m-quasiinvariant with respect to S n if ( x i - x j ) 2 m + 1 divides ( 1 - s ij ) P for all 1 ⩽ i , j ⩽ n . We call the ring of m-quasiinvariants, QI m [ X n ] . We describe a method for constructing a basis for the quotient QI m [ X 3 ] / ( e 1 , e 2 , e 3 ) . This leads to the evaluation of certain binomial determinants that are interesting in their own right.