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Record W4255048748 · doi:10.46298/dmtcs.2910

The topology of restricted partition posets

2011· article· fr· W4255048748 on OpenAlexaff
Richard Ehrenborg, JiYoon Jung

Bibliographic record

VenueDiscrete Mathematics & Theoretical Computer Science · 2011
Typearticle
Languagefr
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsToronto Metropolitan University
FundersNational Science Foundation
KeywordsMathematicsCombinatoricsPartition (number theory)HomotopyHomology (biology)Symmetric groupPure mathematicsChemistry

Abstract

For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π ^• _{\vec{c}}$ is a wedge of $β\vec{c}$ spheres of the same dimensions, where $β\vec{c}$ is the number of permutations with descent composition ^$\vec{c}$. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module $S^B$ where $B$ is a border strip associated to the composition $\vec{c}$. We also study the filter of pointed set partitions generated by a knapsack integer partitions and show the analogous results on homotopy type and action on the top homology. Pour chaque composition $\vec{c}$ nous montrons que le complexe simplicial des chaînes de l'ensemble ordonné $Π ^• _{\vec{c}}$ des partitions pointées d'un ensemble est un bouquet de $β\vec{c}$ sphères de même dimension, où $β\vec{c}$ est le nombre de permutations ayant la composition de descentes $\vec{c}$. De plus, l'action du groupe symétrique sur le groupe d'homologie de degré maximum est isomorphe au module de Specht $S^B$ où $B$ est la bande frontalière associée à la composition $\vec{c}$. Nous étudions aussi le filtre des partitions pointées d'un ensemble, engendré par des partitions d'entiers de type "sac à dos'' et nous démontrons des résultats analogues pour le type d'homotopie et pour l'action sur le groupe d'homologie de degré maximum.

Stored with the screening record, where it is evidence for the labels above.

How this classification was reachedexpand

The three-model screen

all 5,600 screened works →

All three models called this out of scope.

stratum: french · design weight: 1554.47 (the sample is stratified; any rate computed without the weight is wrong)
Claude Opus 4.8OUT
genre: conceptual
about Canada: no
confidence: high

Pure mathematics on the topology of restricted partition posets; the object is a combinatorial structure.

GPT-5.6 (high)OUT
genre: empirical
about Canada: no
confidence: high

This mathematics paper studies the topology of partition posets, not research itself.

Grok 4.5OUT
genre: conceptual
about Canada: no
confidence: high

Pure combinatorial topology of restricted partition posets; mathematics domain.

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)0.000
metaresearch head score (Gemma)0.001
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 score0.012
Threshold uncertainty score0.000

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0010.001
Science and technology studies0.0010.002
Scholarly communication0.0030.004
Open science0.0010.003
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0120.001

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 head0.030
GPT teacher head0.296
Teacher spread0.266 · 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
Published2011
Admission routes1
Has abstractyes

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