Recursive Sorting in Lattices

The direct application of the definition of sorting in lattices [1] is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a sequence. This alternative formulation is inspired by the identity ( n k ) = ( n−1 k−1 ) + ( n−1 k ) that underlies Pascal’s triangle. It provides quadratic complexity and is in fact a generalization of insertion sort for lattices.