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Effective results on the size and structure of sumsets

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  • UserAled Walker (King's London)
  • ClockThursday 24 February 2022, 14:30-15:30
  • HouseMR12.

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Given a finite set A of integer lattice points in d-dimensional space, in 1992 Khovanskii proved that the size of the iterated sumset NA is given exactly by a polynomial P(N) of degree at most d (once N is sufficiently large). But what does ‘sufficiently large’ mean in practice? Khovanskii’s original proof was ineffective. Via other methods, effective bounds have been proved in a few special cases: when d = 1, due to Nathanson; when the convex hull of A is a d-simplex, due to Curran-Goldmakher; and when |A| = d + 2, also due to Curran-Goldmakher. In this talk I will discuss joint work with Andrew Granville and George Shakan, in which we proved an effective bound in the general setting. I will also discuss our related results on the structure of NA (for large N).

This talk is part of the Combinatorics Seminar series.

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