Quasiinvariants of S3

Authors:
Jason Bandlow;Gregg Musiker
Affiliations:
Mathematics Department, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA;Mathematics Department, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 1
Cited 1

Enumerative combinatorics

Enumerative combinatorics

A new characterization for the m-quasiinvariants of Sn and explicit basis for two row hook shapes

Journal of Combinatorial Theory Series A

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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 (xi - xj)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.