Equivariant unimodality of inverse Z-polynomials of matroids
AI-assisted, unrefereed candidate research note. A representation-ring truncation identity proves equivariant unimodality of inverse Z-polynomials for finite loopless matroids with arbitrary finite group actions. A separate corollary extends the result to looped matroids under the stated ranked-flat-lattice convention. The argument explicitly credits the known scalar truncation mechanism and uses the established equivariant inverse Kazhdan–Lusztig positivity theorem. Immediate consequences include a primitive-multiplicity equality criterion and a noncanonical commuting sl2 action. These do not establish a canonical geometric model or strong equivariant log-concavity. Bounded prior-art checks do not establish historical priority.
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-06
- DOI
- https://doi.org/10.5281/zenodo.23995560
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- preprint