bibkey: debski2026barrycades authors: Michał Dębski; Jarosław Grytczuk; Paweł Naroski; Bartłomiej Pawlik; Jakub Przybyło; Małgorzata Śleszyńska-Nowak year: 2026 title: “Finite and infinite barrycades” doi: 10.48550/arXiv.2609.18476 url: https://arxiv.org/abs/2609.18476v1 claim: “The paper defines greedy quasi-barrycade rows and prints Conjecture 2, including A2(i) = A1(i) + 1 for every i >= 3.” strata_touched:

• D5/S3/ArithSums/DebskiBarrycadeOmittedElementRefutation license: citation-only triage: anchor

Finite and infinite barrycades

Michał Dębski, Jarosław Grytczuk, Paweł Naroski, Bartłomiej Pawlik, Jakub Przybyło, and Małgorzata Śleszyńska-Nowak, arXiv:2609.18476v1 (2026).

The paper defines quasi-permutations, their partial-sum sets, and the greedy N-quasi-barrycade. Section 3.1 states Conjecture 2. The second printed statement asserts A2(i) = A1(i) + 1 for every i >= 3, while the preceding observation uses i >= 4. The printed row rho_3 is (4, 3, 1, 5, 6, …), omits 2, and therefore gives A1(3) = 2 and A2(3) = 4.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2609.18476
• Versioned article: https://arxiv.org/abs/2609.18476v1