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This is a Quantitative Study study.

September 17, 2025Open Access

Improved stability for the size and structure of iterated sumsets in \ (Zᵈ\)

Puntos clave

The research improves bounds for the size and structure of iterated sumsets dramatically, indicating substantial progress.
Key improvements include enhancements to both effective bounds for size and structural characteristics of sumsets.
Methodologies include rigorous mathematical analysis and exploitation of polynomial frameworks for iterated sumsets.
The findings may enable deeper insights into combinatorial number theory and related mathematical disciplines.

Resumen

Let \ (A Zᵈ\) be a finite set. It is known that the sumset \ (NA\) has predictable size (\ (NA = PA (N) \) for some \ (PA (X) QX\) ) and structure (all of the lattice points in some finite cone other than all of the lattice points in a finite collection of exceptional subcones), once \ (N\) is larger than some threshold. In previous work, the first effective bounds for both of these thresholds were established, for an arbitrary set \ (A\). In this article we substantially improve each of these bounds, coming much closer to the corresponding lower bounds known. Mathematics Subject Classifications: 11P21, 05B10, 11B13, 11P70, 05A16Keywords: Sumsets, Set addition, Khovanskii polynomial, Structure Theorem, Explicit Bounds

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Cite This Study

Granville et al. (Fri,) studied this question.

synapsesocial.com/papers/68d4605131b076d99fa5fc49 https://doi.org/https://doi.org/10.5070/c65365564

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