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The paper deals with special partitions of whole numbers in the following form: given a sequence of pairs {[Gi;Di]} of positive integers in which the Gi form a strictly increasing sequence, sums of the form ∑niGi, with 0 ≤ ni ≤ Di, are considered. The correspondence[nk ... n0] → ∑i≤k niGidefines then a mapping α from a set M of numerals, called Neugebauer symbols, satisfying 0 ≤ ni ≤ Di, into the set W of all non-negative integers. In M, initial zeros are supressed and M is ordered in the usual...
For any and any , a graph is introduced. Vertices of are -tuples over and two -tuples are adjacent if they are in a certain relation. These graphs are graphs of a particular variant of the Tower of Hanoi problem. Namely, the graphs are isomorphic to the graphs of the Tower of Hanoi problem. It is proved that there are at most two shortest paths between any two vertices of . Together with a formula for the distance, this result is used to compute the distance between two vertices in...
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