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
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preprint

Equivariant unimodality of inverse Z-polynomials of matroids

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Equivariant unimodality of inverse Z-polynomials of matroids

preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
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Equivariant unimodality of inverse Z-polynomials of matroids · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS