Work

Exact Action Depth in a Two-Probe Partition Planner: An n + 1 Diameter Law on Partition Lattices

Year: 2026

Type: preprint

Abstract: We prove the exact worst-case action depth of a two-probe planner on the partition lattice: [ D_2(n)=n+1 \qquad (n\ge5). ] The result is achieved by matching structural upper and lower bounds, with explicit extremal families, mechanical certificates, and a source-level Lean 4 formalization.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22394897

Author: lenoir, benjamin

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7208812796

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