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The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

Euler's 6n+1 theorem states that every prime of the form 6n+1, (i.e., 7, 13, 19, 31, 37, 43, 61, 67, ..., which are also the primes of the form 3n+1; OEIS A002476) can be ...

The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

If a fixed point is added to each group of a special complete series, then the resulting series is complete.

The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix ...

A p×q submatrix of an m×n matrix (with p<=m, q<=n) is a p×q matrix formed by taking a block of the entries of this size from the original matrix.

A node which is one graph edge further away from a given node in a rooted tree.