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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

26 votes

Is the matrix $\left({2m\choose 2j-i}\right)_{i,j=1}^{2m-1}$ nonsingular?

The Lindstrom-Gessel-Viennot lemma says that the number of families of nonintersecting lattice paths can be counted by a determinant. Let $a_i = (2m-i,i)$. Let $b_j = (2m-2j,-2m+2j)$. Then the number …
Douglas Zare's user avatar
7 votes
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The average number of people that can sit on a bench of a given length.

Assume that the process stops when someone can't fit. I believe the distribution of the amount of overshoot is known as a ladder height distribution, and that this is in Feller's classic text, but I …
Douglas Zare's user avatar