# 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,
brendan.mckay@anu.edu.au

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