### Digital search trees with m trees: Level polynomials and insertion costs

*Helmut Prodinger*

#### Abstract

We adapt a novel idea of Cichon's related to Approximate Counting to
the present instance of Digital Search Trees, by using
m (instead of one) such trees. We investigate the level
polynomials, which have as coefficients the expected numbers of data
on a given level, and the insertion costs. The level polynomials can
be precisely described, thanks to formulæ from
q-analysis. The asymptotics of expectation and variance
of the insertion cost are fairly standard these days and done with
Rice's method.

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