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A note on iterated sumsets races

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arxiv 2505.11233 v1 pith:27B3S5PU submitted 2025-05-16 math.NT math.CO

Paul Péringuey , Anne de Roton This is my paper · ORCID
classification math.NTmath.CO
keywords noteciteiteratedkravitzracessumsetsanswersbetter
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abstract

This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer $n$, there are finite sets of integers $A$ and $B$ with same diameter such that the signs of the elements of the sequence $(|hA|-|hB|)_h$ changes at least $n$ times. Kravitz proved in \cite{Kravitz} a much better result. This brief and modest note may serve as a stepping stone towards his work.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Finer control on relative sizes of iterated sumsets

    math.CO 2025-06 conditional novelty 7.0 of 10

    For any infinite abelian group G and any integers m_1,...,m_H, finite sets A,B exist such that |hA| - |hB| = m_h for every h.

  2. Additive sumset sizes with tetrahedral differences

    math.NT 2025-07 conditional novelty 6.0 of 10

    For each h and i0 from 0 to h-1, the set {0,1,h+1,(h+1-i0)(h+1)} has h-fold sumset size binomial(h+3,3) minus binomial(i0+2,3).

  3. Triangular and tetrahedral number differences of sumset sizes in additive number theory

    math.NT 2025-06 conditional novelty 5.0 of 10

    For 4-element sets of integers, the most popular h-fold sumset sizes appear to equal C(h+3,3) minus the first h tetrahedral numbers, but only computer experiments are given.

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