Universal series for dihedral group coinvariant rings
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916956434595840 |
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| author | Lentfer, John |
| author_facet | Lentfer, John |
| contents | In 1994, Alfano determined a monomial basis, bigraded Hilbert series, and bigraded Frobenius series for the ring of diagonal dihedral group coinvariants $R^{(2,0)}_{\mathfrak{I}_{2}(n)}$. Using diagonal supersymmetry, we determine a universal multigraded character series, universal multigraded Hilbert series, and monomial basis for the generalization to any $k$ sets of bosonic variables and $j$ sets of fermionic variables $R^{(k,j)}_{\mathfrak{I}_{2}(n)}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_15054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal series for dihedral group coinvariant rings Lentfer, John Combinatorics 05E10 (Primary) 05E05, 05A15 (Secondary) In 1994, Alfano determined a monomial basis, bigraded Hilbert series, and bigraded Frobenius series for the ring of diagonal dihedral group coinvariants $R^{(2,0)}_{\mathfrak{I}_{2}(n)}$. Using diagonal supersymmetry, we determine a universal multigraded character series, universal multigraded Hilbert series, and monomial basis for the generalization to any $k$ sets of bosonic variables and $j$ sets of fermionic variables $R^{(k,j)}_{\mathfrak{I}_{2}(n)}$. |
| title | Universal series for dihedral group coinvariant rings |
| topic | Combinatorics 05E10 (Primary) 05E05, 05A15 (Secondary) |
| url | https://arxiv.org/abs/2509.15054 |