MétaCan
Menu
Back to cohort
Record W1934564046 · doi:10.37236/2902

On the Relationship between Pipe Dreams and Permutation Words

2013· article· en· W1934564046 on OpenAlexaff
Cameron Marcott

Bibliographic record

VenueThe Electronic Journal of Combinatorics · 2013
Typearticle
Languageen
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsUniversity of Waterloo
FundersSt. Olaf College
KeywordsBijectionPermutation (music)PolyominoMathematicsCombinatoricsWord (group theory)Set (abstract data type)Distributive propertyLattice (music)Discrete mathematicsPure mathematicsGeometryComputer scienceRegular polygon

Abstract

fetched live from OpenAlex

Pipe dreams represent permutations pictorially as a series of crossing pipes. Recent applications of pipe dreams include the calculation of Schubert polynomials, fillings of moon polyominoes, and in the combinatorics of antidiagonal simplicial complexes. These applications associate pipe dreams to words of elementary symmetric transpositions via a canonical mapping. However, this canonical mapping is by no means the only way of mapping pipe dreams to permutation words. We define sensical mappings from pipe dreams to words and prove sensical mappings are in bijection with standard shifted tableaux of triangular shape. We characterize the set of pipe dreams associated to a given word (under any sensical map) using step ladder moves. These moves induce a partial order on the set of pipe dreams mapping to a given word, yielding a distributive lattice.

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 imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.003
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.007
Threshold uncertainty score0.022

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.003
Meta-epidemiology (narrow)0.0000.001
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.001
Science and technology studies0.0020.005
Scholarly communication0.0030.005
Open science0.0010.003
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0070.001

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 head0.038
GPT teacher head0.299
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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations1
Published2013
Admission routes1
Has abstractyes

Explore more

Same venueThe Electronic Journal of CombinatoricsSame topicAdvanced Combinatorial MathematicsFrench-language works237,207