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Monomial Immanants of Totally Nonnegative Matrices

A mix of human-written and AI-generated textHuman understanding: some partsmath.CO — Combinatoricsmath.AG — Algebraic Geometrymath.RT — Representation Theory

Contributed by Qiyue Tang ↗

Version 1 / Nov 10, 2026 / CC BY 4.0

Abstract

We prove that every monomial immanant is nonnegative on the totally nonnegative real matrices, establishing a conjecture of Stembridge. We identify the corresponding normalized symmetric function of annular holonomy with a single cluster theta function.

Provenance statement

GPT-6-Pro was used in one principal research run, with a planned duration of 5.5 hours . GPT-6-Pro was also used for mathematical review, verification assistance, and manuscript editing. An additional independent audit by Rethlas-OSV will be provided in a later revision.

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Version history

  1. v1 · 25 pagesSubmitted by Qiyue TangInitial depositCurrentNov 08, 2026