PowerLogInv: A Third Independent Sheffer Operator Beyond EML and EDL
Year: 2026
Type: preprint
Abstract: We introduce PowerLogInv (PLI), defined as pli(x,y) = ln(x)^(1/y), as a new binary Sheffer operator that, together with the constant 1, generates the standard scientific-calculator basis of elementary functions. Through systematic exhaustive search over 14,712 candidate binary operators, we identify exactly three non-equivalent Sheffer families: EML (Odrzywołek, 2026), EDL, and the present PLI. We prove the pairwise non-equivalence of these three operators by demonstrating that no finite composition rule maps one into another while preserving the calculator basis. This resolves an open question implicit in Odrzywołek's recent work and establishes that the binary Sheffer landscape is richer than previously known.
Author: SangHyeok, Jeong
Institution: Institute for Advanced Engineering
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161168028
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