Bibliographic record
Abstract
This paper is a contribution to the study of hereditary classes of relational structures, these classes being quasi-ordered by embeddability. It deals with the specific case of ordered sets of width two and the corresponding bichains and incomparability graphs. Several open problems about hereditary classes of relational structures which have been considered over the years have positive answer in this case. For example, well-quasi-ordered hereditary classes of finite bipartite permutation graphs, respectively finite 321-avoiding permutations, have been characterized by Korpelainen, Lozin and Mayhill, respectively by Albert, Brignall, Ruškuc and Vatter. We provide another proof of the results mentioned above. It is based on the existence of a countable universal poset of width two, obtained by the first author in 1978, his notion of multichainability (1978) (a kind of analog to letter-graphs), and metric properties of incomparability graphs. Using Laver's theorem (1971) on better-quasi-ordering (bqo) of countable chains we prove that a wqo hereditary class of finite or countable bipartite permutation graphs is necessarily bqo. This gives a positive answer to a conjecture of Nash-Williams (1965) in this case. We extend a previous result of Albert et al. by proving that if a hereditary class of finite, respectively countable, bipartite permutation graphs is wqo, respectively bqo, then the corresponding hereditary classes of posets of width at most two and bichains are wqo, respectively bqo. Several notions of labelled wqo are also considered. We prove that they are all equivalent in the case of bipartite permutation graphs, posets of width at most two and the corresponding bichains. We characterize hereditary classes of finite bipartite permutation graphs which remain wqo when labels from a wqo are added.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
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".