On maximal antihierarchic sets of integers

AbstractWe write the nonnegative integers in a fixed base b ⪖ 2, and call two such integers c and d comparable if each digit of c is at least as big as the respective digit of d, or vice versa; otherwise we say that c and d are uncomparable. A set of pairwise uncomparable integers will be called antihierarchic.The paper contains explicit and asymptotic formulae as well as upper and lower bounds for the cardinality of maximal antihierarchic setsS ⊆ {1, 2, ..., n} for given n