Search Results for ""

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

Let C denote a chain complex, a portion of which is shown below: ...->C_(n+1)->C_n->C_(n-1)->.... Let H_n(C)=kerpartial_n/Impartial_(n+1) denotes the nth homology group. Then ...

The generalization of the Schönflies theorem to n dimensions. A smoothly embedded n-hypersphere in an (n+1)-hypersphere separates the (n+1)-hypersphere into two components, ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

A root having multiplicity n=1 is called a simple root. For example, f(z)=(z-1)(z-2) has a simple root at z_0=1, but g=(z-1)^2 has a root of multiplicity 2 at z_0=1, which is ...

A sequence of numbers alpha_n is said to be uncorrelated if it satisfies lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_m^2=1 lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_malpha_(k+m)=0 for ...

The de Bruijn constant, also called the Copson-de Bruijn constant, is the minimal constant c=1.1064957714... (OEIS A113276) such that the inequality ...

The Desargues graph is the cubic symmetric graph on 20 vertices and 30 edges illustrated above in several embeddings. It is isomorphic to the generalized Petersen graph ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...