Permutations of the Natural Numbers with Prescribed Difference Multisets

We study permutations π of the natural numbers for which the numbers π(n) are chosen greedily under the restriction that the differences π(n)−n belong to a given (multi)subset M of Z for all n ∈ S, a given subset of N. Various combinatorial properties of such permutations (for quite general M and S) are exhibited and others conjectured. Our results generalise to a large extent known facts in the case M = Z, S = N, where the permutation π arises in the study of the game of Wythoff Nim