bibkey: callan2023inversion authors: David Callan, Toufik Mansour year: 2023 title: “Inversion Sequences Avoiding Quadruple Length-3 Patterns” doi: 10.5281/zenodo.8399694 url: https://math.colgate.edu/~integers/x78/x78.pdf claim: “Class 152: {010, 100, 102, 210} ∼_I {011, 201, 210}; Class 207: {100, 101, 110, 201} ∼_I {101, 110, 120, 210}.” strata_touched:

• D5/S3/Combinatorics/InversionSeq/InversionSeqClass152 license: citation-only triage: anchor

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

The paper classifies the sets of four patterns of length three by the number of inversion sequences of each length that avoid them, and shows that the number of I-Wilf-equivalence classes among quadruples is at least 212 and at most 215, leaving three comparisons open.

Verified locator

DOI: 10.5281/zenodo.8399694

URL: https://math.colgate.edu/~integers/x78/x78.pdf

• Locator: Section 1, an inversion sequence of length n is e_1 ⋯ e_n with 0 ≤ e_i < i; two sets of patterns are I-Wilf-equivalent when they are avoided by equally many inversion sequences of every length.
• Locator: Section 1, Conjecture 1: Class 152, {010, 100, 102, 210} ∼_I {011, 201, 210}; Class 166, {010, 100, 110, 201} ∼_I {010, 101, 120, 201}; Class 207, {100, 101, 110, 201} ∼_I {101, 110, 120, 210}; checked by the authors up to n = 13.
• Locator: Table 1, the three comparisons are marked “still open”.

Reading of the statement

Both classes of Class 152 have 1, 1, 2, 5, 15, 50, 176, 638, 2354, 8789, 33099 elements for n = 0, …, 10, which is (1 + Σ_{j<n} binom(2j, j))/2 for n ≥ 1.

Bounded prior-resolution evidence

Read on 2026-10-01: Asinowski and Polley (arXiv:2501.11781, Theorem 11) settle Class 166 of Conjecture 1; none of the later papers located by citation and full-text search treats Class 152 or Class 207. This is a bounded negative finding.