Bibliographic record
Abstract
Immanants are a generalization of the well-studied determinant and permanent. Although the combinatorial interpretations for the determinant and permanent have been studied in excess, there remain few combinatorial interpretations for the immanant. \n \nThe main objective of this thesis is to consider the immanant, and its possible combinatorial interpretations, in terms of recursive structures on the character. This thesis presents a comprehensive view of previous interpretations of immanants. Furthermore, it discusses algebraic techniques that may be used to investigate further into the combinatorial aspects of the immanant. \n \nWe consider the Temperley-Lieb algebra and the class of immanants over the elements of this algebra. Combinatorial tools including the Temperley-Lieb algebra and Kauffman diagrams will be used in a number of interpretations. In particular, we extend some results for the permanent and determinant based on the $R$-weighted planar network construction, where $R$ is a convenient ring, by Clearman, Shelton, and Skandera. This thesis also presents some cases in which this construction cannot be extended. Finally, we present some extensions to combinatorial interpretations on certain classes of tableaux, as well as certain classes of matrices.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".