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An analytic refinement of results from complex analysis such as those codified by Picard's little theorem, Picard's great theorem, and the Weierstrass-Casorati theorem.

A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

The lines joining the vertices A, B, and C of a given triangle DeltaABC with the circumcenters of the triangles DeltaBCO, DeltaCAO, and DeltaABO (where O is the circumcenter ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of ...

If a graph G has n graph vertices such that every pair of the n graph vertices which are not joined by a graph edge has a sum of valences which is >=n, then G is Hamiltonian. ...

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

The n-Pasechnik graph is a strongly regular graph on (4n-1)^2 vertices constructed from a skew Hadamard matrix of order 4n. It has regular parameters . The 1-Pasechnik is ...