We study the polytopes of binary n-strings that encode (positive) integers that are not divisible by a partivular positive integer p - the indivisibility polytopes, as well as the more general "clipped cubes". Also, we discuss a potential application to factoring. Finally, we present some...

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds.