Asymptotics for Incidence Matrix Classes

  • Peter Cameron
  • Thomas Prellberg
  • Dudley Stark


We define incidence matrices to be zero-one matrices with no zero rows or columns. We are interested in counting incidence matrices with a given number of ones, irrespective of the number of 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 some of these classes as $n\to\infty$.

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