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A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

Consider a clause (disjunction of literals) obtained from those of a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then an atomic statement ...

Consider a clause (disjunction of literals) obtained from those of a first-order logic sentential formula Phi in Skolemized form forall x_1... forall x_nS, then a clause ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

If G is a perfect group, then the group center of the quotient group G/Z(G), where Z(G) is the group center of G, is the trivial group.

Johnson solid J_(10).

Johnson solid J_(22).

Let A=a_(ik) be an arbitrary n×n nonsingular matrix with real elements and determinant |A|, then |A|^2<=product_(i=1)^n(sum_(k=1)^na_(ik)^2).

Let |A| be an n×n determinant with complex (or real) elements a_(ij), then |A|!=0 if |a_(ii)|>sum_(j=1; j!=i)^n|a_(ij)|.

The Hajós number h(G) of a graph G is the maximum k such that G contains a subdivision of the complete graph K_k.