Consider a p-periodic diﬀerence equation xn+1 = fn(xn) with a global attractor. How does a permutation [fσ(p−1), . . . , fσ(1), fσ(0)] of the maps aﬀect the global attractor? In this paper, we limit this general question to the Beverton-Holt model with p-periodic harvesting. We ﬁx a set of harvesting quotas and give ourselves the liberty to permute them. The total harvesting yield is unchanged by the permutation, but the population geometric-mean may ﬂuctuate. We investigate this notion and characterize the cases in which a permutation of the harvesting quotas has no eﬀect or tangible eﬀect on the population geometric-mean. In particular, as long as persistence is assured, all permutations within the dihedral group give same population geometric-mean. Other permutations may change the population geometric-mean. A characterization theorem has been obtained based on block reﬂections in the harvesting quotas. Finally, we associate directed graphs to the various permutations, then give the complete characterization when the periodicity of the system is four or ﬁve.