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I heard a talk at Indiana University last March by Timothy Chow. Here's his abstract, which seems to give a negative answer to your question about rectangles whose sides have non-integer ratio: It i …

I'll take a stab at answering my own question. The missing “something” in the edited version of my question appears to be the mutual information of one or more events, denoted $I(A,B,C,...)$. More p …

The following web site might be useful to you: The Stony Brook Algorithm Repository, http://www.cs.sunysb.edu/~algorith/

Another book is Classification Algorithms for Codes and Designs by Kaski and Östergård. The authors are responsible for the recent complete enumeration of Steiner triple systems of order 19. (All 11 …

Here's an article available online: "Isomorph-free exhaustive generation" by Brendan D. McKay. See cs.anu.edu.au/~bdm/papers/orderly.pdf The author also wrote the graph isomorphism package 'nauty …

To answer your question about interesting combinatorial objects: Your Sylvester-Hadamard matrix example generalizes in at least two ways. The incidence matrix of any balanced incomplete block design …

When I teach elementary probability to my finite math students, a common error is to mix up the concepts of disjointness and independence. At some point I thought that it might be helpful to some stu …

From Hadamard's bound the largest possible determinant of an $n\times n$ (0,1) matrix is $h_n=2^{-n}(n+1)^{(n+1)/2}$. The data at http://www.indiana.edu/~maxdet/spectrum.html suggest several conject …

At Scott's request, here's my comment in answer form: The stated conditions imply imply that your two matrices are equivalent. Up to permutation of rows and columns, your diagonal matrix is the Smit …

As pointed out in Robin Chapman's answer and Frederio Poloni's comment thereto, there is a one-to-one map between normalized $n$-by-$n$ $(-1,1)$ matrices and $(n-1)$-by-$(n-1)$ $(0,1)$ matrices under …