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An Extension of the Foata Map to Standard Young Tableaux

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Jim Haglund, Laura Stevens

Combinatorics · Submitted 27 Nov 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that this statistic has the same distribution over SYT(\lambda) as the major index statistic by exhibiting a bijection on SYT(\lambda) in the spirit of the Foata map on permutations.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0611822 (version 1)
Pith IDVSO32NDA, Pith's permanent record of this paper and its review
CitationJim Haglund, Laura Stevens. "An Extension of the Foata Map to Standard Young Tableaux." arXiv:math/0611822 (2006). https://pith.science/paper/VSO32NDA
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,242 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.62 · compares with prior results 0.61 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SYT(\lambda) as the major index statistic by exhibiting a bijection on SYT(\lambda) in the spirit of the Foata map on permutations.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We define an inversion statistic on standard Young tableaux. contribution 1.00 0.95 0.05 asserted 0.99
s1 We prove that this statistic has the same distribution over SYT(\lambda) as the major index statistic by exhibiting a bijection on SYT(\lambda) in the spirit of the Foata map on permutations. result 0.72 0.96 0.89 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SYT(\lambda) as the major index statistic by exhibiting a bijection on SYT(\lambda) in the spirit of the Foata map on permutations.

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