  Simon's classical random-copying model, introduced in 1955, has garnered much
attention for its ability, in spite of an apparent simplicity, to produce
characteristics similar to those observed across the spectrum of complex
systems. Through a discrete-time mechanism in which items are added to a
sequence based upon rich-gets-richer dynamics, Simon demonstrated that the
resulting size distributions of such sequences exhibit power-law tails. The
simplicity of this model arises from the approach by which copying occurs
uniformly over all previous elements in the sequence. Here we propose a
generalization of this model which moves away from this uniform assumption,
instead incorporating memory effects that allow the copying event to occur via
an arbitrary kernel. Through this approach we first demonstrate the potential
to determine further information regarding the structure of sequences from the
classical model before illustrating, via analytical study and numeric
simulation, the flexibility offered by the arbitrary choice of memory.
Furthermore we demonstrate how previously proposed memory-dependent models can
be further studied as specific cases of the proposed framework.
