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A RAT-free ("right angle triangle-free") set is a set of points, no three of which determine a right triangle. Let f(n) be the largest integer such that a RAT-free subset of ...

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.

For a set partition of n elements, the n-character string a_1a_2...a_n in which each character gives the set block (B_0, B_1, ...) in which the corresponding element belongs ...

The d-dimensional rigidity matrix M(G) of a graph G with vertex count n, edge count m in the variables v_i=(x_1,...,x_d) is the m×(dn) matrix with rows indexed by the edges ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

A partition whose conjugate partition is equivalent to itself. The Ferrers diagrams corresponding to the self-conjugate partitions for 3<=n<=10 are illustrated above. The ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

Solid partitions are generalizations of plane partitions. MacMahon (1960) conjectured the generating function for the number of solid partitions was ...