Equivariant unimodality of inverse Z-polynomials of matroids
Year: 2026
Type: preprint
Abstract: 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.
Author: Anonymous
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225426108