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The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

The Robertson-Wegner graph is of the four (5,5)-cage graphs, also called Robertson's cage (Read and Wilson 1998, p. 273). Like the other (5,5)-cages, the Robertson-Wegner ...

n weighings are sufficient to find a bad coin among (3^n-1)/2 coins (Steinhaus 1999, p. 61). vos Savant (1993) gives an algorithm for finding a bad ball among 12 balls in ...

One form of van der Waerden's theorem states that for all positive integers k and r, there exists a constant n(r,k) such that if n_0>=n(r,k) and {1,2,...,n_0} subset C_1 ...

S(nu,z) = int_0^infty(1+t)^(-nu)e^(-zt)dt (1) = z^(nu-1)e^zint_z^inftyu^(-nu)e^(-u)du (2) = z^(nu/2-1)e^(z/2)W_(-nu/2,(1-nu)/2)(z), (3) where W_(k,m)(z) is the Whittaker ...

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

Elementary methods consist of arithmetic, geometry, and high school algebra. These are the only tools that may be used in the branch of number theory known as elementary ...

The imaginary part I[z] of a complex number z=x+iy is the real number multiplying i, so I[x+iy]=y. In terms of z itself, I[z]=(z-z^_)/(2i), where z^_ is the complex conjugate ...

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...