Search Results for ""

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

The Johnson graph J(n,k) has vertices given by the k-subsets of {1,...,n}, with two vertices connected iff their intersection has size k-1. Special classes are summarized in ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

Let A={A_1,A_2,...,A_n} be a union-closed set, then the union-closed set conjecture states that an element exists which belongs to at least n/2 of the sets in A. Sarvate and ...

Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...

If three skew lines all meet three other skew lines, any transversal to the first set of three meets any transversal to the second set of three.

An arrangement of points with no three collinear, or of lines with no three concurrent.

In one dimension, the interval [0,1] is the closed unit interval, the interval (0,1) is the open unit interval, and the intervals (0,1] and [0,1) are half-open unit intervals.

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...