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July 6, 2026Open Access

A Kazhdan–Lusztig interaction formula for nested (non-split) matroids with two cyclic flats

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Authors

MYMitsutoshi Yamada

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Overview

Preprint explores the Kazhdan–Lusztig polynomials in nested matroids, revealing important interactions and implications.

Key Points

  • The aim is to explore the Kazhdan–Lusztig and inverse-KL polynomials for a specific configuration of nested matroids with two cyclic flats.
  • Introduced the interaction formula to measure failure of valuative additivity.
  • Derived closed forms for linear KL coefficients and constant inverse-KL coefficients using hyperplane counts and induction.
  • Developed a generating-function recursion for both coefficients.
  • Closed forms for the linear KL coefficient across all ρ₁ were established (with proof).
  • The constant inverse-KL coefficient was proven via deletion–contraction induction.
  • A general degree law was formulated that relates the interaction at any rank to hyperplane values.

Cite This Study

Mitsutoshi Yamada (2026) studied this question.

synapsesocial.com/papers/6a4b4641997070ff83b5bbfahttps://doi.org/10.5281/zenodo.21198034
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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) matroids2026
  2. 2Deletion formulas for equivariant Kazhdan-Lusztig polynomials of matroids2024
  3. 3Inverse Kazhdan-Lusztig polynomials of matroids need not be log-concave2026
  4. 4The Combinatorics Behind the Leading Kazhdan-Lusztig Coefficients of Braid Matroids2024
  5. 5Log‐concavity of inverse Kazhdan–Lusztig polynomials of paving matroids2026