Asymptotic enumeration of incidence matrices

Abstract

We discuss the problem of counting {\em 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 $n\to \infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.

jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthday