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Record W2741277981 · doi:10.46298/dmtcs.3605

Quasisymmetric Schur functions

2008· article· fr· W2741277981 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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueDiscrete Mathematics & Theoretical Computer Science · 2008
Typearticle
Languagefr
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsOkanagan University CollegeUniversity of British Columbia, Okanagan CampusUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of CanadaNational Science Foundation
KeywordsMathematicsSchur's lemmaSchur algebraCombinatoricsSchur's theoremSchur polynomialSymmetric functionPure mathematicsMacdonald polynomialsOrthogonal polynomialsJacobi polynomialsClassical orthogonal polynomials

Abstract

fetched live from OpenAlex

We introduce a new basis for the algebra of quasisymmetric functions that naturally partitions Schur functions, called quasisymmetric Schur functions. We describe their expansion in terms of fundamental quasisymmetric functions and determine when a quasisymmetric Schur function is equal to a fundamental quasisymmetric function. We conclude by describing a Pieri rule for quasisymmetric Schur functions that naturally generalizes the Pieri rule for Schur functions. Nous étudions une nouvelle base des fonctions quasisymétriques, les fonctions de quasiSchur. Ces fonctions sont obtenues en spécialisant les fonctions de Macdonald dissymétrique. Nous décrivons les compositions que donne une simple fonction quasisymétriques. Nous décrivons aussi une règle par certaines fonctions de Schur.

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.

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)0.004
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Insufficient payload (model declined to judge)
Consensus categoriesScience and technology studies, Insufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.373
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.004
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0010.005
Science and technology studies0.0020.015
Scholarly communication0.0010.001
Open science0.0030.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0020.003

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 head0.028
GPT teacher head0.289
Teacher spread0.261 · 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