6 papers
Universal Hilbert series coefficients of the superspace coinvariant ring
Sylvie Corteel, John Lentfer
The coefficients that determine the Hilbert series of the superspace coinvariant ring are indexed by hook-shaped partitions. We give a manifestly positive combinatorial interpretat…
Type fermionic coinvariant rings
Yuhan Jiang, John Lentfer
Let denote the hyperoctahedral group. The type coinvariant rings are quotients of the ring of polynomials in sets of commu…
Diagonal supersymmetry for coinvariant rings
John Lentfer
For finite groups , we show that bosonic-fermionic coinvariant rings have a natural -module structure. In particular, we show that t…
The sign character of the triagonal fermionic coinvariant ring
John Lentfer
We determine the trigraded multiplicity of the sign character of the triagonal fermionic coinvariant ring . As a corollary, this proves a conjecture of Bergeron (2020)…
A conjectural basis for the -bosonic-fermionic coinvariant ring
John Lentfer
We give the first conjectural construction of a monomial basis for the coinvariant ring , for the symmetric group acting on one set of bosonic (commuting) and tw…
Universal series for dihedral group coinvariant rings
John Lentfer
In 1994, Alfano determined a monomial basis, bigraded Hilbert series, and bigraded Frobenius series for the ring of diagonal dihedral group coinvariants $R^{(2,0)}_{\mathfrak{I}_{2…