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Let the vertices of a graph G be numbered with distinct integers 1 to |G|. Then the dilation of G is the maximum (absolute) difference between integers assigned to adjacent ...

If r is a root of a nonzero polynomial equation a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0, (1) where the a_is are integers (or equivalently, rational numbers) and r satisfies no ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

As shown by Morse and Feshbach (1953), the Helmholtz differential equation is separable in confocal paraboloidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in prolate spheroidal coordinates.

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

Assume that n numbered pancakes are stacked, and that a spatula can be used to reverse the order of the top k pancakes for 2<=k<=n. Then the pancake sorting problem asks how ...

In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...