Metadata
bibkey: sheppard2025a381524
authors: Mike Sheppard
year: 2025
title: "OEIS A381524, smallest exponent of a maximal absolute Hermite coefficient"
doi: null
url: https://oeis.org/A381524/internal?rev=18
claim: "Conjecture: Differences are either +1 or -1."
strata_touched:
- D5/S3/Analytic/Polynomial/HermiteAbsoluteMode
license: citation-only
triage: anchor
Verified locator
Source: https://oeis.org/A381524/internal?rev=18, revision 18, Definition and Comments, with offset zero. The definition is “Smallest exponent of x of maximal coefficient (ignoring signs) in Hermite polynomial of order n.” The independent conjecture is “Differences are either +1 or -1.”
The source’s HermiteH convention and its examples fix physicists normalization. Its order-five example chooses exponent three. At order eight the absolute coefficients at exponents two and four tie, and the source chooses two. The formal target keeps this smallest-index tie convention over all coefficients from zero through n, including zero coefficients, for every natural n.
The bounded inspected sources do not supply an exact whole-target solver. The specific Dudeja–Hsu Lemma 35 citation remains unidentified; inspection of arXiv:2204.07526 does not close that citation gap. No complete literature search, global openness certification or priority claim is made.
The complete external assertion is preregistered at https://github.com/the-omega-institute/trureturing/issues/25789#issuecomment-6586906062.