Quasiinvariants of S3

Jason Bandlow, Gregg Musiker

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)281-298
Number of pages18
JournalJournal of Combinatorial Theory. Series A
Volume109
Issue number2
DOIs
StatePublished - Feb 2005

Keywords

  • Binomial coefficients
  • Determinant evaluations
  • Non-intersecting lattice paths
  • Symmetric functions
  • Symmetric group
  • m-quasiinvariants

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