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The ascending chain condition, commonly abbreviated "A.C.C.," for a partially ordered set X requires that all increasing sequences in X become eventually constant. A module M ...

A sequence of primes q_1<q_2<...<q_k is a Cunningham chain of the first kind (second kind) of length k if q_(i+1)=2q_i+1 (q_(i+1)=2q_i-1) for i=1, ..., k-1. Cunningham primes ...

The Fibonacci chain map is defined as x_(n+1) = -1/(x_n+epsilon+alphasgn[frac(n(phi-1))-(phi-1)]) (1) phi_(n+1) = frac(phi_n+phi-1), (2) where frac(x) is the fractional part, ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

The series of Sturm functions arising in application of the Sturm theorem.

Any sum of a selection of Pi_ks, where Pi_k denotes a k-D polytope.

A k-chain whose bounding (k-1)-chain vanishes.

A number n for which a shortest chain exists (which is also a Hansen chain) is called a Hansen number.

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

For a partial order, the size of the longest chain is called the length.