The Davenport constant and first precise arithmetical results

Abstract

In this chapter we study the Davenport constant, a classical combinatorial invariant which has been investigated since the 1960s (see [115, 105, 31, 108, 103]). From the very beginning the investigation of this invariant was related also to arithmetical problems (it is reported in [108] that in 1966 H. Davenport asked for D(G), since it is the largest number of prime ideals occurring in the prime ideal decomposition of an irreducible integer in an algebraic number field with ideal class group G). However, it has turned out that this and related invariants occur in many branches of combinatorics, number theory and geometry (see [52] for a recent survey, and [99, 33] for the relationship with invariant theory).