A (p, q)-ary chain is a special type of chain partition of integers with parts of the form (p^a q^b) for some fixed integers p and q. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound m. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of m, asymptotically independent of max(p, q), and we provide an efficient algorithm to compute it.
On the maximal weight of (p,q)-ary chain-partitions with bounded parts
DISANTO, FILIPPO;
2014-01-01
Abstract
A (p, q)-ary chain is a special type of chain partition of integers with parts of the form (p^a q^b) for some fixed integers p and q. In this note, we are interested in the maximal weight of such partitions when their parts are distinct and cannot exceed a given bound m. Characterizing the cases where the greedy choice fails, we prove that this maximal weight is, as a function of m, asymptotically independent of max(p, q), and we provide an efficient algorithm to compute it.File in questo prodotto:
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