Partitions of an Integer into Powers
Copyright policy )Partitions of an Integer into Powers
In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also give a tree structure which allow efficient and simple enumeration of the partitions of an integer.
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], [INFO] Computer Science [cs], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], distributive lattice, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Distributive Lattice, Discrete Dynamical Models, discrete dynamical models, [info.info-cg] computer science [cs]/computational geometry [cs.cg], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], QA1-939, FOS: Mathematics, Mathematics - Combinatorics, [INFO]Computer Science [cs], integer partition, lattice, [math.math-co] mathematics [math]/combinatorics [math.co], [info] computer science [cs], Lattice, chip firing game, Chip Firing Game, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], composition, Integer partition, Combinatorics (math.CO), Mathematics, Composition, Computer Science - Discrete Mathematics
FOS: Computer and information sciences, Discrete Mathematics (cs.DM), [info.info-dm] computer science [cs]/discrete mathematics [cs.dm], [INFO] Computer Science [cs], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], distributive lattice, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Distributive Lattice, Discrete Dynamical Models, discrete dynamical models, [info.info-cg] computer science [cs]/computational geometry [cs.cg], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], QA1-939, FOS: Mathematics, Mathematics - Combinatorics, [INFO]Computer Science [cs], integer partition, lattice, [math.math-co] mathematics [math]/combinatorics [math.co], [info] computer science [cs], Lattice, chip firing game, Chip Firing Game, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], composition, Integer partition, Combinatorics (math.CO), Mathematics, Composition, Computer Science - Discrete Mathematics
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