Search Results for ""

How far can a stack of n books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_n for n books (in terms of ...

The complex conjugate of a complex number z=a+bi is defined to be z^_=a-bi. (1) The conjugate matrix of a matrix A=(a_(ij)) is the matrix obtained by replacing each element ...

A cube can be divided into n subcubes for only n=1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, and n>=48 (OEIS A014544; Hadwiger 1946; Scott 1947; Gardner 1992, ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

The conjecture that the number of alternating sign matrices "bordered" by +1s A_n is explicitly given by the formula A_n=product_(j=0)^(n-1)((3j+1)!)/((n+j)!). This ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

A bicubic graph is a bipartite cubic graph. Tutte (1971) conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic ...

There are several related series that are known as the binomial series. The most general is (x+a)^nu=sum_(k=0)^infty(nu; k)x^ka^(nu-k), (1) where (nu; k) is a binomial ...