Is the share of a central place in the population of the area, served by this central place, a constant for all levels of the Christaller's hierarchy?
One of the conditions of the central place theory is the assumption of a constant k parameter - a share of a central place in the population of the area served by this central place - for all levels of the Christaller's hierarchy. Nevertheless, we did not find a rigorous proof of this assertion (underlying the Beckmann-Parr equation) in the bibliography on the central place theory. If this condition is assumed true, it also remains unclear - whether for all or only for strictly defined k-values. We have established that if the chosen K-value of the Christaller's hierarchy is constant at every lattice level, the Beckmann-Parr equation holds for all meaningful values of k. At the same time we found that the range of k-values for an ideal Christaller's lattice is bounded above by not an asymptote at k = 1, but an exact almost twice smaller value equal to Since the latter changes very slightly during a radical rearrangement of the lattice from K = 3 to K = 7, we can state that we have discovered the new nonstrict invariant in the central place theory - the maximum value of k.