bibkey: callan2025ascent authors: David Callan, Toufik Mansour year: 2025 title: “Ascent Sequences and Weak Ascent Sequences Avoiding a Quadruple of Length-3 Patterns” doi: 10.5281/zenodo.17144266 url: https://math.colgate.edu/~integers/z80/z80.pdf claim: “Class 215 of the WA-Wilf classification of quadruples of length-3 patterns is left open.” strata_touched:

• D5/S3/Combinatorics/WeakAscent/WeakAscentClass215 license: citation-only triage: anchor

Callan and Mansour, ascent and weak ascent sequences avoiding quadruples of length-3 patterns

The paper classifies the quadruples of length-3 patterns by the numbers of ascent sequences and of weak ascent sequences of each length that avoid them. For weak ascent sequences it determines all classes but one, so that the number of WA-Wilf-equivalence classes is 228 or 229.

Verified locator

DOI: 10.5281/zenodo.17144266

URL: https://math.colgate.edu/~integers/z80/z80.pdf

• Locator: Section 1, a weak ascent sequence is a_1 ⋯ a_n with a_1 = 0 and a_i ≤ 1 + wasc(a_1 ⋯ a_{i−1}), where wasc counts the positions j with a_j ≤ a_{j+1}.
• Locator: Section 1, Theorem 2: the number WAS4 of WA-Wilf-equivalence classes among quadruples of length-3 patterns is either 228 or 229, because the status of Class 215 is left open.
• Locator: Table 2, Class 215: {100, 101, 110, 201} and {021, 101, 201, 210}, marked “Open”.

Reading of the statement

Both sets of Class 215 are avoided by 1, 1, 2, 6, 20, 71, 264, 1015, 4002, 16094, 65758, 272208 weak ascent sequences of lengths n = 0, …, 11 (OEIS A049124).

Bounded prior-resolution evidence

Read on 2026-10-01: no located later paper, OEIS entry or public repository settles Class 215. This is a bounded negative finding.