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Asymptotics for incidence matrix classes

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Peter Cameron, Thomas Prellberg, Dudley Stark

Combinatorics · Submitted 7 Oct 2005

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

The authors' main claim We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$.

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arXiv IDmath/0510155 (version 2)
Pith IDPXXXCI52, Pith's permanent record of this paper and its review
CitationDudley Stark, Peter Cameron, Thomas Prellberg. "Asymptotics for incidence matrix classes." arXiv:math/0510155 (2005). https://pith.science/paper/PXXXCI52
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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, 2,918 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We define {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$.

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 {\em incidence matrices} to be zero-one matrices with no zero rows or columns. background 0.88 0.66 0.03 asserted 0.99
s1 A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. contribution 0.76 0.55 0.05 asserted 0.85
s2 We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$. result 0.58 0.96 0.83 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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  • 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 {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$.

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