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Record W2951814084 · doi:10.46298/dmtcs.2942

Row-strict quasisymmetric Schur functions

2011· article· en· W2951814084 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueDiscrete Mathematics & Theoretical Computer Science · 2011
Typearticle
Languageen
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsMathematicsCombinatoricsSchur's theoremBasis (linear algebra)Schur's lemmaBase (topology)Function (biology)Pure mathematicsOrthogonal polynomialsGeometryMathematical analysisClassical orthogonal polynomials

Abstract

fetched live from OpenAlex

Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the $\textit{quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the $\textit{row-strict quasisymmetric Schur function basis}$ which are generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through row-strict tableaux. We describe the relationship between this new basis and other known bases for quasisymmetric functions, as well as its relationship to Schur polynomials. We obtain a refinement of the omega transform operator as a result of these relationships. Haglund, Luoto, Mason, et van Willigenburg ont introduit une base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "column-strict'' (ordre strict sur les colonnes). Nous introduisons une nouvelle base pour les fonctions quasi-symétriques appelée $\textit{base des fonctions de Schur quasi-symétriques "row-strict''}$, qui sont construites en remplissant des diagrammes de compositions, d'une manière très semblable à la construction des fonctions de Schur à partir des tableaux "row-strict'' (ordre strict sur les lignes). Nous décrivons la relation entre cette nouvelle base et d'autres bases connues pour les fonctions quasi-symétriques, ainsi que ses relations avec les polynômes de Schur. Nous obtenons un raffinement de l'opérateur oméga comme conséquence de ces relations.

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Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.003
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.504
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.003
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.003
Science and technology studies0.0010.003
Scholarly communication0.0000.001
Open science0.0020.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.001

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.

Opus teacher head0.042
GPT teacher head0.294
Teacher spread0.252 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it