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Condensed configurations and valuative matroid invariants
Abstract
Condensed configurations are compact incidence data obtained by grouping the cyclic flats of a matroid. We show that their inverse incidence matrices give explicit Schubert expansions and hence determine every valuative or covaluative matroid invariant. For the extended binary Golay matroid, this unexpectedly produces non-real-rooted Kazhdan-Lusztig and Z-polynomials. To our knowledge, the latter is the first counterexample in the literature.
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BibTeX
@misc{eberhardt2026condensed,
title = {{Condensed configurations and valuative matroid invariants}},
author = {Jens Niklas Eberhardt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20903},
eprint = {2609.20903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20903},
}
RIS
TY - UNPB
TI - Condensed configurations and valuative matroid invariants
AU - Jens Niklas Eberhardt
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20903
UR - https://arxiv.org/abs/2609.20903
AB - Condensed configurations are compact incidence data obtained by grouping the cyclic flats of a matroid. We show that their inverse incidence matrices give explicit Schubert expansions and hence determine every valuative or covaluative matroid invariant. For the extended binary Golay matroid, this unexpectedly produces non-real-rooted Kazhdan-Lusztig and Z-polynomials. To our knowledge, the latter is the first counterexample in the literature.
ER -