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A q-Analog of Foulke's conjecture

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François Bergeron

Combinatorics · Submitted 25 Feb 2016

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

The authors' main claim At $q=0$, we get back the original statement of Foulkes, and we show that our version holds at $q=1$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1602.08134 (version 4)
Pith IDFOAQNMJB, Pith's permanent record of this paper and its review
CitationFran\c{c}ois Bergeron. "A q-Analog of Foulke's conjecture." arXiv:1602.08134 (2016). https://pith.science/paper/FOAQNMJB
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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, 3,628 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete homogeneous symmetric functions $h_n(\mathbf{x})$ in Foulkes conjecture. At $q=0$, we get back the original statement of Foulkes, and we show that our version holds at $q=1$. We discuss further supporting evidence, as well as various generalizations.

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 propose a $q$-analog of classical plethystic conjectures due to Foulkes. contribution 1.00 0.91 0.27 asserted 0.87
s1 In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete homogeneous symmetric functions $h_n(\mathbf{x})$ in Foulkes conjecture. contribution 0.98 0.64 0.24 asserted 0.95
s2 At $q=0$, we get back the original statement of Foulkes, and we show that our version holds at $q=1$. result 0.98 0.94 0.31 asserted 1.00
s3 We discuss further supporting evidence, as well as various generalizations. contribution 0.83 0.73 0.05 unclear 0.68

What kind of paper the classifier reports this is: theoretical result 0.68 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • 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 propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete homogeneous symmetric functions $h_n(\mathbf{x})$ in Foulkes conjecture. At $q=0$, we get back the original statement of Foulkes, and we show that our version holds at $q=1$. We discuss further supporting evidence, as well as various generalizations.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 1 sentence without a confident label

Cites as background 4 papers

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