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Preprints, Working Papers, ... Year : 2023

Optimal Bounds on the Growth of Iterated Sumsets in Abelian Semigroups

Abstract

We provide optimal upper bounds on the growth of iterated sumsets hA = A + • • • + A for finite subsets A of abelian semigroups. More precisely, we show that the new upper bounds recently derived from Macaulay's theorem in commutative algebra are best possible, i.e., are actually reached by suitable subsets of suitable abelian semigroups. Our constructions, in a multiplicative setting, are based on certain specific monomial ideals in polynomial algebras and on their deformation into appropriate binomial ideals via Gröbner bases.
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Dates and versions

hal-04243232 , version 1 (16-10-2023)

Identifiers

  • HAL Id : hal-04243232 , version 1

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Shalom Eliahou, Eshita Mazumdar. Optimal Bounds on the Growth of Iterated Sumsets in Abelian Semigroups. 2023. ⟨hal-04243232⟩
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