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Record W2962849036 · doi:10.1090/memo/1072

Spectra of Symmetrized Shuffling Operators

2014· book· en· W2962849036 on OpenAlex

Why this work is in the frame

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

Bibliographic record

Venuenot available
Typebook
Languageen
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsUniversité du Québec à Montréal
FundersAgence Nationale de la Recherche
KeywordsShufflingHyperplaneMathematicsCombinatoricsEquivariant mapBibliographyIndex (typography)Random walkDiscrete mathematicsAlgebra over a fieldPure mathematicsComputer scienceStatisticsLibrary scienceWorld Wide Web

Abstract

fetched live from OpenAlex

Abstract. For a finite real reflection group W and a W-orbit O of flats in its reflection arrangement – or equivalently a conjugacy class of its parabolic subgroups – we introduce a statistic noninvO(w) on w in W that counts the number of “O-noninversions ” of w. This generalizes the classical (non-)inversion statistic for permutations w in the symmetric group Sn. We then study the operator νO of right-multiplication within the group algebra CW by the element that has noninvO(w) as its coefficient on w. We reinterpret νO geometrically in terms of the arrangement of reflecting hyperplanes for W, and more generally, for any real arrangement of linear hyperplanes. At this level of generality, one finds that, after appropriate scaling, νO corresponds to a Markov chain on the chambers of the arrangement. We show that νO is self-adjoint and positive semidefinite, via two explicit factorizations into a symmetrized form pitpi. In one such factorization, the matrix pi is a generalization of the projection of a simplex onto the linear ordering polytope from the theory of social choice. In the other factorization of νO as pitpi, the matrix pi is the transition matrix for one of the well-studied Bidigare-Hanlon-Rockmore random walks on the chambers of an ar-

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)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.107
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.038
GPT teacher head0.308
Teacher spread0.270 · 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

Quick stats

Citations12
Published2014
Admission routes1
Has abstractyes

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