Extremal graphs for the list-coloring version of a theorem of Nordhaus and Gaddum

In this paper we propose a simple strategy for memory management of multidimensional arrays whose entries are known to be invariant under a special permutation group P of the coordinates. The group P is not known in advance and is entered as a parameter of the procedure. The strategy is to obtain a partition of Lδn, the relevant lattice of positive integer points in Rn, into parts which behaves well under the action of P. The partition is controlled by a hierarchy of combinatorial objects, forming a tree. The leaves of this tree are identified with some vertices of a digraph encoding special decreasing sequences. Both this digraph and the leaf-identified tree, denoted Lδn >P, are instances of Nijenhuis-Wilf combinatorial families. The members of Lδn/P become maximal paths in Lδn/P. This fact enables the quick computation of the address rδp(δ), for δ ∈ Lδn/P.