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Equitable partitions of Latin-square graphs

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R. A. Bailey, Peter J. Cameron, Alexander L. Gavrilyuk, Sergey V. Goryainov

Combinatorics · Submitted 3 Feb 2018

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

The authors' main claim We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue $-3$.

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arXiv ID1802.01001 (version 1)
Pith IDPOXGEBZH, Pith's permanent record of this paper and its review
CitationAlexander L. Gavrilyuk, Peter J. Cameron, R. A. Bailey, Sergey V. Goryainov. "Equitable partitions of Latin-square graphs." arXiv:1802.01001 (2018). https://pith.science/paper/POXGEBZH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,595 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.64 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.38 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue $-3$.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue $-3$. contribution 0.87 0.95 0.84 asserted 1.00

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

We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue $-3$.

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