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Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

The symbol union , used for the union of sets, and, sometimes, also for the logical connective OR instead of the symbol v (vee). In fact, for any two sets A and B x in A ...

A two-person game where each of the players can take as long as he likes to prepare his move, but the other can take advantage of his hesitation. In this conflict situation, ...

Efron's dice are set of four nontransitive dice such that the probabilities of A winning against B, B against C, C against D, and D against A are all the same. The images ...

A deeper result than the Hardy-Ramanujan theorem. Let N(x,a,b) be the number of integers in [n,x] such that inequality a<=(omega(n)-lnlnn)/(sqrt(lnlnn))<=b (1) holds, where ...

Let f(z) = z+a_1+a_2z^(-1)+a_3z^(-2)+... (1) = zsum_(n=0)^(infty)a_nz^(-n) (2) = zg(1/z) (3) be a Laurent polynomial with a_0=1. Then the Faber polynomial P_m(f) in f(z) of ...

Let f(x) be a monic polynomial of degree d with discriminant Delta. Then an odd integer n with (n,f(0)Delta)=1 is called a Frobenius pseudoprime with respect to f(x) if it ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

A purple cow is a confirming instance of the hypothesis that all crows are black.