Asymptotic enumeration of incidence matrices

Peter Cameron; Thomas Prellberg; Dudley Stark

doi:10.1088/1742-6596/42/1/007

Asymptotic enumeration of incidence matrices

Peter Cameron^*, Thomas Prellberg, Dudley Stark

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss the problem of counting incidence matrices, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with n ones as n → ∞. We also give refined results for the asymptotic number of i × j incidence matrices with n ones.

Original language	English
Article number	007
Pages (from-to)	59-70
Number of pages	12
Journal	Journal of Physics: Conference Series
Volume	42
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/42/1/007
Publication status	Published - 1 Jul 2006

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title = "Asymptotic enumeration of incidence matrices",

abstract = "We discuss the problem of counting incidence matrices, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with n ones as n → ∞. We also give refined results for the asymptotic number of i × j incidence matrices with n ones.",

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AB - We discuss the problem of counting incidence matrices, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with n ones as n → ∞. We also give refined results for the asymptotic number of i × j incidence matrices with n ones.

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Asymptotic enumeration of incidence matrices

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