English

Universal series for dihedral group coinvariant rings

Combinatorics 2025-09-19 v1

Abstract

In 1994, Alfano determined a monomial basis, bigraded Hilbert series, and bigraded Frobenius series for the ring of diagonal dihedral group coinvariants RI2(n)(2,0)R^{(2,0)}_{\mathfrak{I}_{2}(n)}. Using diagonal supersymmetry, we determine a universal multigraded character series, universal multigraded Hilbert series, and monomial basis for the generalization to any kk sets of bosonic variables and jj sets of fermionic variables RI2(n)(k,j)R^{(k,j)}_{\mathfrak{I}_{2}(n)}.

Keywords

Cite

@article{arxiv.2509.15054,
  title  = {Universal series for dihedral group coinvariant rings},
  author = {John Lentfer},
  journal= {arXiv preprint arXiv:2509.15054},
  year   = {2025}
}

Comments

15 pages, 2 figures, comments are welcome