Combinatorics on Words: 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings
Bibliographic record
Abstract
Palindromic length of a word is defined as the smallest number n such that the word can be written as a product of n palindromes.It has been conjectured that every aperiodic infinite word has factors of arbitrarily high palindromic length.A stronger variant of this conjecture claims that every aperiodic infinite word has also prefixes of arbitrarily high palindromic length.We prove that these two conjectures are equivalent.More specifically, we prove that if every prefix of a word is a product of n palindromes, then every factor of the word is a product of 2n palindromes.Our proof quite naturally leads us to compare the properties of palindromic length in free monoids and in free groups.For example, the palindromic lengths of a word and its conjugate can be arbitrarily far apart in a free monoid, but in a free group they are almost the same.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.008 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.011 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.113 | 0.031 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".