  We give a unified analysis of linear probing hashing with a general bucket
size. We use both a combinatorial approach, giving exact formulas for
generating functions, and a probabilistic approach, giving simple derivations
of asymptotic results. Both approaches complement nicely, and give a good
insight in the relation between linear probing and random walks. A key
methodological contribution, at the core of Analytic Combinatorics, is the use
of the symbolic method (based on q-calculus) to directly derive the generating
functions to analyze.
