The paper introduces the sets R_Z(h,k) and R_{Z^n}(h,k) collecting all possible cardinalities of hA for |A|=k, studies their complexity, and supplies a diameter-compression algorithm that preserves |hA|.
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math.NT 3years
2025 3verdicts
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Conditions are examined for equality hA = intersection hA_q where A is the intersection of a strictly decreasing sequence of sets A_q in an additive abelian semigroup.
Constructs infinite families of k-element integer sets and computes their h-fold sumset sizes for h,k ≥ 3.
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Compression and complexity for sumset sizes in additive number theory
The paper introduces the sets R_Z(h,k) and R_{Z^n}(h,k) collecting all possible cardinalities of hA for |A|=k, studies their complexity, and supplies a diameter-compression algorithm that preserves |hA|.
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Intersections of sumsets in additive number theory
Conditions are examined for equality hA = intersection hA_q where A is the intersection of a strictly decreasing sequence of sets A_q in an additive abelian semigroup.
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Explicit sumset sizes in additive number theory
Constructs infinite families of k-element integer sets and computes their h-fold sumset sizes for h,k ≥ 3.