Equivariant gamma-positivity conjecture for matroid Chow rings
Equivariant gamma-positivity conjecture for matroid Chow rings
Let be a loopless matroid of rank , let be a group of automorphisms of , and let
be its complexified matroid Chow ring, with each graded piece carrying the induced -module structure. Equivariant gamma-positivity conjecture. The ring is -equivariantly -positive, namely its equivariant Hilbert series admits a -expansion whose coefficients are classes of genuine complex representations of . This is the formal version of the equivariant conjecture attributed to Angarone, Nathanson, and Reiner; the source does not state that it has been resolved.
Sources & referencesView supporting material
Primary source
Hsin-Chieh Liao, “Equivariant gamma-positivity of matroid Chow rings”, arXiv:2408.00745 (2026).
Additional references
3 papers in this index state this conjecture (2008–2024). The statement above is taken from the most recent of them; the others are arXiv:2309.14312, arXiv:0801.2776.
Progress summary
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