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Let P be a prime ideal in D_m not containing m. Then (Phi(P))=P^(sumtsigma_t^(-1)), where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of ...

A topological sort is a permutation p of the vertices of a graph such that an edge {i,j} implies that i appears before j in p (Skiena 1990, p. 208). Only acyclic digraphs can ...

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

An algorithm for computing an Egyptian fraction.

An estimator of the actual values of population.

A conjecture for the eigenvalues of modular forms under Hecke operators.

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph G together with any edges whose endpoints are both in this ...