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ii) Simplification: If AX [up arrow] BY either by column catenation or by row catenation with A and B being of same size, then A [up arrow] B and X [up arrow] Y.
Let A, B, X, Y be partial arrays such that AX [up arrow] BY, either by column catenation or by row catenation.
2] are nonnegative integers, using column catenation.
Catenation of x and y with respect to a merging function m : [SIGMA] [SIGMA] [SIGMA] [right arrow] [SIGMA] is defined as
m] catenation from figures in X [subset or equal to] [[SIGMA].
An interesting extension of our results would be to consider figures with no merging function, where catenation is a partial operation defined for those figures that do not overlap when catenated.
Additional Key Words and Phrases: Catenation, data structures, double-ended queue, persistent data structures, purely functional data structures, purely functional queues, queue, stack
Perhaps the simplest and probably the most important example of combining data structures is catenation (appending) of lists.
The dramatic effect of the catenation pattern may be attributed to their nonlinear and asymmetric structures.