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July 13, 2026Open Access

A Kazhdan–Lusztig interaction formula for nested (non-split) matroids

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Authors

MYMitsutoshi Yamada

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Overview

This preprint demonstrates an interaction formula for nested matroids, revealing new invariants and recursive relationships.

Key Points

  • The aim is to derive an explicit interaction formula for Kazhdan-Lusztig polynomials in the context of nested matroids with nontrivial cyclic flats.
  • Developed closed forms for linear KL coefficients and constant inverse-KL coefficients.
  • Established a flat-count recursion valid for all nullity orderings and lengths.
  • Implemented a verification engine in Python for reproducibility of computational claims.
  • Proved an explicit alternating multiple-binomial formula for inclusion-exclusion interactions at every rank.
  • Demonstrated a single-binomial closed form for low inverse-KL coefficients when nullity is greater than or equal to 2.
  • Identified the threshold where the single-binomial structure of low inverse-KL coefficients breaks down.

Cite This Study

Mitsutoshi Yamada (2026) studied this question.

synapsesocial.com/papers/6a54835d475c38bf615a5edbhttps://doi.org/10.5281/zenodo.21307660
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A Kazhdan–Lusztig interaction formula for nested (non-split) matroids with two cyclic flats2026
  2. 2Deletion formulas for equivariant Kazhdan-Lusztig polynomials of matroids2024
  3. 3Inverse Kazhdan-Lusztig polynomials of matroids need not be log-concave2026
  4. 4Hilbert–Poincaré series of matroid Chow rings and intersection cohomology2024 · 14 citations
  5. 5The Combinatorics Behind the Leading Kazhdan-Lusztig Coefficients of Braid Matroids2024