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The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...

Prellberg (2001) noted that the limit c=lim_(n->infty)(T_n)/(B_nexp{1/2[W(n)]^2})=2.2394331040... (OEIS A143307) exists, where T_n is a Takeuchi number, B_n is a Bell number, ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

Smarandache sequences are any of a number of simply generated integer sequences resembling those considered in published works by Smarandache such as the consecutive number ...

The number of partitions of n in which no parts are multiples of k is sometimes denoted b_k(n) (Gordon and Ono 1997). b_k(n) is also the number of partitions of n into at ...

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...