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If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

An algorithm for computing an Egyptian fraction.

A submodule S of a module M such that for any proper submodule T of M, the submodule generated by S union T is not the entire module M. S is also called superfluous submodule.

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A roll of two 1s (the lowest roll possible) on a pair of six-sided dice. The probability of rolling snake eyes is 1/36, or 2.777...%.

The 6-polyiamond illustrated above.