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An inequality on broken chessboards

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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K. De Naeghel, N. Marconnet

Combinatorics · Submitted 5 Jan 2006

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

The authors' main claim In this note we characterize all pairs (b,w) which arise in this way.

how it is stated · asserted 0.99 read the record →

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arXiv IDmath/0601094 (version 1)
Pith IDOFT2SUZX, Pith's permanent record of this paper and its review
CitationK. De Naeghel, N. Marconnet. "An inequality on broken chessboards." arXiv:math/0601094 (2006). https://pith.science/paper/OFT2SUZX
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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, 5,372 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.78 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.66 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

For any partition of a positive integer we consider the chess (or draughts) colouring of its associated Ferrers graph. Let b denote the total number of black unit squares, and w the number of white squares. In this note we characterize all pairs (b,w) which arise in this way. This simple combinatorical result was discovered by characterizing Hilbert series of certain right modules over cubic three-dimensional Artin-Schelter algebras. However in this note we present a purely combinatorical proof. The result is (at least partially) known in literature, however we found it interesting to present an elementary proof. All additional references and remarks will be mostly appreciated.

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 For any partition of a positive integer we consider the chess (or draughts) colouring of its associated Ferrers graph. background 0.83 0.36 0.03 asserted 0.74
s1 Let b denote the total number of black unit squares, and w the number of white squares. background 0.87 0.26 0.02 asserted 0.70
s2 In this note we characterize all pairs (b,w) which arise in this way. contribution 0.83 0.90 0.57 asserted 0.99
s3 This simple combinatorical result was discovered by characterizing Hilbert series of certain right modules over cubic three-dimensional Artin-Schelter algebras. background 0.59 0.72 0.05 asserted 1.00
s4 However in this note we present a purely combinatorical proof. method 0.57 0.91 0.06 asserted 1.00
s5 The result is (at least partially) known in literature, however we found it interesting to present an elementary proof. background 0.80 0.82 0.03 asserted 0.68
s6 All additional references and remarks will be mostly appreciated. future work 0.93 0.09 0.01 unclear 0.66

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

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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

For any partition of a positive integer we consider the chess (or draughts) colouring of its associated Ferrers graph. Let b denote the total number of black unit squares, and w the number of white squares. In this note we characterize all pairs (b,w) which arise in this way. This simple combinatorical result was discovered by characterizing Hilbert series of certain right modules over cubic three-dimensional Artin-Schelter algebras. However in this note we present a purely combinatorical proof. The result is (at least partially) known in literature, however we found it interesting to present an elementary proof. All additional references and remarks will be mostly appreciated.

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