Word of length 110 over {0, 1, 3, 6}
Display: drawn for the equivalent alphabet translated by -2 (drift removed).
0 1 0 6 0 1 0 3 6 0 6 1 0 1 3 1 6 0 1 6 3 6 0 1 0 3 6 3 1 0 1 6 0 1 0 3 0 1 0 6 0 3 6 0 6 1 0 3 0 1 0 6 1 6 3 6 1 0 6 0 3 6 0 6 1 6 3 6 1 6 0 1 3 1 6 0 6 3 0 6 0 1 3 1 6 0 1 0 3 0 1 0 6 0 3 6 3 1 6 0 6 3 1 6 1 0 6 1 6 3
Alphabet {0, 1, 3, 6}
closed The exact maximum additive-square-free word length over this alphabet is 110. exhaustive search (dfs_a179.c), 2,338,999,808 nodes; tree exhausted with max length exactly 110, attained by 14 words (7 reversal pairs, current record among them); 111.6 s single-threaded CPU (Ryzen 9 5950X). Independently cross-checked: node counts match a separate Python enumerator through depth 14, and all 14 maximal words re-verified square-free in Python.
Closure claims
- accepted max 110 claimed by David Renshaw, 2026-08-27 · evidence — exhaustive search (dfs_a179.c), 2,338,999,808 nodes; tree exhausted with max length exactly 110, attained by 14 words (7 reversal pairs, current record among them); 111.6 s single-threaded CPU (Ryzen 9 5950X). Independently cross-checked: node counts match a separate Python enumerator through depth 14, and all 14 maximal words re-verified square-free in Python.
Record history
- 110 (first) — Aayush Rajasekaran, 2026-08-20
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