# Counts of semiregular 0-1 matrices

This page is an appendix to the paper Asymptotic enumeration of 0-1 matrices with equal row sums and equal column sums, by E. Rod Canfield and Brendan D. McKay, Electronic Journal of Combinatorics, 12 (2005) #R29.

Define B(m,s;n,t) to be the number of 0-1 matrices with m rows and n columns such that each row has sum s and each column has sum t. There is no notion of equivalence.

#### Values of B(m,s;n,t)

The text file Bvals.txt contains the values of B(m,s;n,t) for all m,n ≤ 30, apart from the values which can be deduced from other values using the rules B(m,s,n,t) = B(m,n-s,n,m-t) = B(n,t,m,s) = B(n,m-t,m,n-s) and B(m,0,n,0) = 1.

The Maple input text file Bvals.maple contains the same values and also knows how to apply the extra rules. In addition, it can compute any value of B(m,s;n,t) for t ≤ 2 or s = t = 3. To use it in a Maple session (console or worksheet), input it using the "read" command. Then a procedure B(m,s,n,t) will have been defined. In case the procedure does not know how to compute the value, it returns the string "unknown".

In addition, Bvals.maple defines a procedure Best(m,s,n,t) whose output is a "best guess" of B(m,s;n,t) and a real interval which is conjectured to hold the value of B(m,s;n,t). Note that this conjecture has not been proved and no guarantees are made.

Page Master: Brendan McKay, bdm@cs.anu.edu.au and http://cs.anu.edu.au/~bdm.

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