# catenate

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## cat·en·ate

(kat'en-āt),
To connect in a series of links like a chain; for example, two rings of mitochondrial DNA are often catenated.
[L. catenatus, chained together, fr. catena, chain]

## cat·en·ate

(kat'ĕn-āt)
To connect in a series of links like a chain.
[L. catenatus, chained together, fr. catena, chain]
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References in periodicals archive ?
Supposing that A and B are k-conjugate, then, by definition, there exist nonnegative integers [k.sub.l], [k.sub.2] whose sum is k and partial arrays X and Y such that [mathematical expression not reproducible] with error set [mathematical expression not reproducible] with error set [E.sub.2] using row catenation or column catenation accordingly.
Then, [mathematical expression not reproducible] with error set [E.sub.1] and [mathematical expression not reproducible] with error set [E'.sub.2] = {(i + number of rows of X, j)/(i, j) [member of] [E.sub.2]} or [E'.sub.2] = {(i, j + number of columns of X)/(i, j) [member of] [E.sub.2]} according to row or column catenation and so, for Z = X, we have AZ [up arrow] [sub.[less than or equal to]k]ZB.
Once catenation is added as an operation, the problem of making stacks or deques persistent becomes much harder; all the methods mentioned above fail.
The green-yellow-red mechanism applied to an underlying linear structure suffices to add constant-time catenation to stacks.
In this section, we present a real-time, purely functional implementation of deques without catenation. This example illustrates our ideas in a simple setting, and provides an alternative to the implementation based on a pair of incrementally copied stacks, which was described in Section 2.
Our next goal is a deque structure that supports fast catenation. Since catenable steques (deques without eject) are easier to implement than catenable deques, we discuss catenable steques here, and delay our discussion of a structure that supports the full set of operations to Section 6.
Specifically, to form the catenation [s.sub.3] of two steques [s.sub.1] and [s.sub.2], we apply the appropriate one of the following three cases:
A catenation of two regular steques takes O(1) time and results in a regular steque.
A catenation of two semiregular deques produces a semiregular deque.
To support catenation as well as flip requires a little more work.
A final open problem is to devise a purely functional implementation of finger search trees (random-access lists) with constant-time catenation. Our best solution to this problem has O(log log n) catenation time [Kaplan and Tarjan 1996].
Persistent lists with catenation via recursive slow-down.

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